OLUWASEUN ADEYEYE
Universiti Utara Malaysia, School of Quantitaive Sciences, Faculty Member
Block methods have been adopted in studies for solving first and higher order differential equations due to its impressive accuracy property. Taking a step further to improve this accuracy, researchers have considered the inclusion of... more
Block methods have been adopted in studies for solving first and higher order differential equations due to its impressive accuracy property. Taking a step further to improve this accuracy, researchers have considered the inclusion of higher-derivative terms in the block method, although this has been limited to the presence of one higher-derivative term in previous studies. Hence, this article aims at better accuracy by introducing two higher-derivative terms in the block method. In addition, this article presents a scheme with generalised step length such that there is flexibility on the choice of step length when developing the block method. The generalised step length scheme is adopted to develop a three-step block method for solving first-order fuzzy initial value problems. Its properties to ensure convergence and to show the region of absolute stability is investigated, and problems relating to charging and discharging of capacitor are considered. The absolute error shows the ...
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The aim of this work is to present the magnetized flow of Casson nanomaterials confined due to porous space with stability framework. The slip mechanism for thermal concentration diffusion has been elaborated. The shrinking surface with... more
The aim of this work is to present the magnetized flow of Casson nanomaterials confined due to porous space with stability framework. The slip mechanism for thermal concentration diffusion has been elaborated. The shrinking surface with exponential velocity induced the flow. The new block method is imposed for the simulation process. The resulting systems of ODEs of the third and second orders are solved jointly using the block method, which is appropriate for dealing with the different orders of the system of ODEs. From a physical standpoint, graphs of different profiles for increasing values of the various applied parameters have been drawn and discussed in detail. To satisfy the infinite boundary conditions, we assigned numerical values such that all profiles converge asymptotically at [Formula: see text]. Furthermore, numerical results from the block method show that velocity profile declines with rising Casson and porous parameter values, as expected. It is noted that the heat ...
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This study is an investigation of an exponentially decaying internal heat generation rate and free nanoparticle movement on the boundary layer. The equations describing the hydromagnetic flow and heat transfer in a viscous nanofluid... more
This study is an investigation of an exponentially decaying internal heat generation rate and free nanoparticle movement on the boundary layer. The equations describing the hydromagnetic flow and heat transfer in a viscous nanofluid moving over an isothermal stretching sheet are solved using a novel numerical approach. A comparison of flow and heat transfer characteristics between an actively controlled (AC) and a passively controlled (PC) nanoparticle concentration boundary is considered. The boundary value partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The system of ODEs is solved using a new block method without having to reduce the equivalent system to first‐order equations. The solutions are verified using the spectral local linearization method and further validation of the results is confirmed by comparing the current results, for some limiting cases, with those in existing literature. The solutions obtained using the block method are in good agreement with the solution obtained using the spectral local linearization method. The results are in good agreement with existing findings in previous studies. The solutions obtained using the AC and PC nanoparticle concentration boundary conditions are analyzed.
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A method of collocation and interpolation of the power series approximate solution at some grid and off-grid points is considered to generate a continuous linear multistep method for the solution of general second order initial value... more
A method of collocation and interpolation of the power series approximate solution at some grid and off-grid points is considered to generate a continuous linear multistep method for the solution of general second order initial value problems at constant step size. We use continuous block method to generate independent solutions which serves as predictors at selected points within the interval of integration. The efficiency of the proposed method was tested and was found to compete favorably with the existing methods.
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Block methods have been very suitable and useful in the solution of higher order ordinary differential equations (ODEs). This is because it gives a higher level of accuracy than conventional methods of reduction of higher order ODEs or... more
Block methods have been very suitable and useful in the solution of higher order ordinary differential equations (ODEs). This is because it gives a higher level of accuracy than conventional methods of reduction of higher order ODEs or predictor-corrector methods. However, the step by step process needed in developing this method based on either the stepnumber or the order of the ODE under consideration is rigorous. Hence, the introduction of an algorithm that will bypass this setback is expedient and thus the aim of this article. Mathematics Subject Classifications: 65L05, 65L06, 65L10
This study introduces new operational matrices to approximate the solution of first and second order delay differential equations (DDEs) using Said-Ball polynomials (SBP). To obtain the required approximate solution, the DDEs are... more
This study introduces new operational matrices to approximate the solution of first and second order delay differential equations (DDEs) using Said-Ball polynomials (SBP). To obtain the required approximate solution, the DDEs are transformed to a simplified set of algebraic equations with the adoption of the residual correction procedure (RCP) for error estimation of the SBP operational matrices. Some examples are given to demonstrate the employability of the new method and a comparison is made with the existing results. The new approach of adopting Said-Ball operational matrix displayed impressive results when compared in terms of absolute error with previous studies.
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The application of a hybrid block method to solving third order ordinary differential equations is considered in this article. The hybrid method is developed for a set of equidistant hybrid points using a new generalized linear block... more
The application of a hybrid block method to solving third order ordinary differential equations is considered in this article. The hybrid method is developed for a set of equidistant hybrid points using a new generalized linear block method (GLBM). The equations for the GLBM takes a similar form as the conventional linear multistep method, however the form produces the needed family of schemes required to simultaneously evaluate the solution of the third order ordinary differential equations at individual grid points in a self-starting mode. The hybrid block method obtained using GLBM is investigated and the block method possesses good basic property of a numerical method which is displayed in the numerical results obtained. Furthermore, the comparison to works of the past authors shows that the new hybrid block gives impressive results in terms of error and consistency particularly for large intervals.
The introduction of new approaches to numerically approximate higher order ordinary differential equations (ODEs) is vastly being explored in recent literature. The reason for adopting these numerical approaches is because some of these... more
The introduction of new approaches to numerically approximate higher order ordinary differential equations (ODEs) is vastly being explored in recent literature. The reason for adopting these numerical approaches is because some of these higher order ODEs fail to have an approximate solution or the current numerical approach being adopted has less accuracy. The application of an implicit block method for solving fourth order ordinary differential equations (ODEs) is considered in this article. The solution encompasses both initial and boundary value problems of fourth order ODEs. The implicit block method is developed for a set of six equidistant points using a new linear block approach (LBA). The LBA produces the required family of six-step schemes to simultaneously evaluate the solution of the fourth order ODEs at individual grid points in a self-starting mode. The basic properties of the implicit block method are investigated, and the block method is seen to satisfy the property of convergence which is displayed in the numerical results obtained. Furthermore, in comparison to works of past authors the implicit block method gives more impressive results.
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Block methods have been seen to be an adequate numerical method for finding the approximate solution to second order ordinary differential equations. Thus, this article presents a block method of maximal order for the direct solution of... more
Block methods have been seen to be an adequate numerical method for finding the approximate solution to second order ordinary differential equations. Thus, this article presents a block method of maximal order for the direct solution of second order initial and boundary value problems. Taylor series expansion approach is adopted for the derivation of the block methods. From the numerical results obtained, this new block method performs better than previous numerical methods in existence in terms of accuracy, when compared to the exact solution of the numerical problems considered.
Block methods as an approach for solving higher order ordinary differential equations (ODEs) have been seen to be very useful in recent literature. However, the development of the block methods for higher order, such as fourth order ODEs... more
Block methods as an approach for solving higher order ordinary differential equations (ODEs) have been seen to be very useful in recent literature. However, the development of the block methods for higher order, such as fourth order ODEs is seen to include a lot of steps and transformations. This is irrespective of the approach adopted; be it interpolation, numerical integration or Taylor series. Hence, this study investigates into producing an algorithm that can produce the desired block method directly for any value of the stepnumber k, whose computational complexity is also shown.
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This article introduces two approaches to develop block methods for solving second order ordinary differential equations directly. Both approaches, namely a new linear block approach and the modified Taylor series approach are capable of... more
This article introduces two approaches to develop block methods for solving second order ordinary differential equations directly. Both approaches, namely a new linear block approach and the modified Taylor series approach are capable of producing a family of methods that will simultaneously approximate the solutions of any ordinary differential equation at the respective grid points of the block method. The computational complexities of both approaches are examined, and the results show the new linear block approach require less computations compared to the modified Taylor series approach.
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The processes of diffusion and reaction play essential roles in numerous system dynamics. Consequently, the solutions of reaction–diffusion equations have gained much attention because of not only their occurrence in many fields of... more
The processes of diffusion and reaction play essential roles in numerous system dynamics. Consequently, the solutions of reaction–diffusion equations have gained much attention because of not only their occurrence in many fields of science but also the existence of important properties and information in the solutions. However, despite the wide range of numerical methods explored for approximating solutions, the adoption of block methods is yet to be investigated. Hence, this article introduces a new two-step third–fourth-derivative block method as a numerical approach to solve the reaction–diffusion equation. In order to ensure improved accuracy, the method introduces the concept of nonlinearity in the solution of the linear model through the presence of higher derivatives. The method obtained accurate solutions for the model at varying values of the dimensionless diffusion parameter and saturation parameter. Furthermore, the solutions are also in good agreement with previous solut...
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Second order boundary value problems can be solved directly using block methods.This solution can be implemented with or without the use of starting values. However, a comparison of the effects of starting values on the results gotten... more
Second order boundary value problems can be solved directly using block methods.This solution can be implemented with or without the use of starting values. However, a comparison of the effects of starting values on the results gotten from solving a second order boundary value problem has not been investigated into.Therefore, in this work a two-step block method for the numerical solution of a two-point second order boundary value problem is described. The derivation of the method from Taylor series expansions leads to a family of block matrix equations which are used to solve the boundary value problems.The method is implemented with starting and non-starting values and the results are compared with previously existing methods.The results show an improvement in the accuracy of the method when implemented with starting values.
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Nonlinear boundary value problems (BVPs) are more tedious to solve than their linear counterparts. This is observed in the extra computation required when determining the missing conditions in transforming BVPs to initial value problems.... more
Nonlinear boundary value problems (BVPs) are more tedious to solve than their linear counterparts. This is observed in the extra computation required when determining the missing conditions in transforming BVPs to initial value problems. Although a number of numerical approaches are already existent in literature to solve nonlinear BVPs, this article presents a new block method with improved accuracy to solve nonlinear BVPs. A m+1th-step block method is developed using a modified Taylor series approach to directly solve fourth-order nonlinear boundary value problems (BVPs) where m is the order of the differential equation under consideration. The schemes obtained were combined to simultaneously produce solution to the fourth-order nonlinear BVPs at m+1 points iteratively. The derived block method showed improved accuracy in comparison to previously existing authors when solving the same problems. In addition, the suitability of the m+1th-step block method was displayed in the soluti...
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... have been devoted to the development of various methods for solving (1) directly by various authors such as (DO Awoyemi, 2001; DO Awoyemi and SJ Kayode, 2005; AO Adesanya, 2008; ZA Majid, 2009) and (SJ Kayode, 2010; YA Yahaya and AM... more
... have been devoted to the development of various methods for solving (1) directly by various authors such as (DO Awoyemi, 2001; DO Awoyemi and SJ Kayode, 2005; AO Adesanya, 2008; ZA Majid, 2009) and (SJ Kayode, 2010; YA Yahaya and AM Badmus, 2009) developed a ...
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Various algorithms have been proposed for developing block methods where the most adopted approach is the numerical integration and collocation approaches. However, there is another conventional approach known as the Taylor series... more
Various algorithms have been proposed for developing block methods where the most adopted approach is the numerical integration and collocation approaches. However, there is another conventional approach known as the Taylor series approach, although it was utilised at inception for the development of linear multistep methods for first order differential equations. Thus, this article explores the adoption of this approach through the modification o f t he a forementioned conventional Taylor series approach. A new methodology is then presented for developing block methods, which is a more accurate method for solving second order ordinary differential equations, coined as the Modified Taylor Series (MTS) Approach. A further step is taken by presenting a generalised form of the MTS Approach that produces any k−step block method for solving second order ordinary differential equations. The computational complexity of this approach after being generalised to develop k-step block method for second order ordinary differential equations is calculated and the result shows that the generalised algorithm involves less computational burden, and hence is suitable for adoption when developing block methods for solving second order ordinary differential equations. Specifically, an alternate and easy-to-adopt approach to developing k−step block methods for solving second order ODEs with fewer computations has been introduced in this article with the developed block methods being suitable for solving second order differential equations directly.
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Improved accuracy has been observed in block methods with the presence of higher derivatives when implemented to solve first order and higher order ordinary differential equations. This improvement in accuracy is as a result of the... more
Improved accuracy has been observed in block methods with the presence of higher derivatives when implemented to solve first order and higher order ordinary differential equations. This improvement in accuracy is as a result of the increased order possessed by the higher derivative block method. In this article, a fourth-derivative block method of maximal-order is introduced to solve third order initial and boundary value problems. The block method possesses convergent properties required for any good numerical method and it is suitable for solving third order ODE models. This is evident in its improved performance over other methods in terms of comparison to the exact solution of the numerical problems considered.
A number of authors have considered the solution of second order initial value problems (IVPs) and the adoption of block methods of order eight has been seen to be widely applied. However, these previously developed block methods have... more
A number of authors have considered the solution of second order initial value problems (IVPs) and the adoption of block methods of order eight has been seen to be widely applied. However, these previously developed block methods have considered non-hybrid grid points. Hence, this article presents a new hybrid block method of order eight for solving second order IVPs with an improved level of accuracy when compared to previously existing order eight block methods in terms of error. The methodology employed involves a new generalized algorithm for developing the hybrid block method which is another novel contribution existing in this work. Hence, not only this article presents a new block method that can be adopted when solving real life problems modelled as second order IVPs, it also gives a more convenient algorithm for developing hybrid block methods.
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Improved accuracy has been observed in block methods with the presence of higher derivatives when implemented to solve first order and higher order ordinary differential equations. This improvement in accuracy is as a result of the... more
Improved accuracy has been observed in block methods with the presence of higher derivatives when implemented to
solve first order and higher order ordinary differential equations. This improvement in accuracy is as a result of the increased order
possessed by the higher derivative block method. In this article, a fourth-derivative block method of maximal-order is introduced
to solve third order initial and boundary value problems. The block method possesses convergent properties required for any good
numerical method and it is suitable for solving third order ODE models. This is evident in its improved performance over other
methods in terms of comparison to the exact solution of the numerical problems considered.
solve first order and higher order ordinary differential equations. This improvement in accuracy is as a result of the increased order
possessed by the higher derivative block method. In this article, a fourth-derivative block method of maximal-order is introduced
to solve third order initial and boundary value problems. The block method possesses convergent properties required for any good
numerical method and it is suitable for solving third order ODE models. This is evident in its improved performance over other
methods in terms of comparison to the exact solution of the numerical problems considered.
This article introduces two approaches to develop block methods for solving second order ordinary differential equations directly. Both approaches, namely a new linear block approach and the modified Taylor series approach are capable of... more
This article introduces two approaches to develop block methods for solving second order ordinary differential equations directly. Both approaches, namely a new linear block approach and the modified Taylor series approach are capable of producing a family of methods that will simultaneously approximate the solutions of any ordinary differential equation at the respective grid points of the block method. The computational complexities of both approaches are examined, and the results show the new linear block approach require less computations compared to the modified Taylor series approach.
The application of a hybrid block method to solving third order ordinary differential equations is considered in this article. The hybrid method is developed for a set of equidistant hybrid points using a new generalized linear block... more
The application of a hybrid block method to solving third order ordinary differential equations is considered in this article. The hybrid method is developed for a set of equidistant hybrid points using a new generalized linear block method (GLBM). The equations for the GLBM takes a similar form as the conventional linear multistep method, however the form produces the needed family of schemes required to simultaneously evaluate the solution of the third order ordinary differential equations at individual grid points in a self-starting mode. The hybrid block method obtained using GLBM is investigated and the block method possesses good basic property of a numerical method which is displayed in the numerical results obtained. Furthermore, the comparison to works of the past authors shows that the new hybrid block gives impressive results in terms of error and consistency particularly for large intervals.
The introduction of new approaches to numerically approximate higher order ordinary differential equations (ODEs) is vastly being explored in recent literature. The reason for adopting these numerical approaches is because some of these... more
The introduction of new approaches to numerically approximate higher order ordinary differential equations (ODEs) is vastly being explored in recent literature. The reason for adopting these numerical approaches is because some of these higher order ODEs fail to have an approximate solution or the current numerical approach being adopted has less accuracy. The application of an implicit block method for solving fourth order ordinary differential equations (ODEs) is considered in this article. The solution encompasses both initial and boundary value problems of fourth order ODEs. The implicit block method is developed for a set of six equidistant points using a new linear block approach (LBA). The LBA produces the required family of six-step schemes to simultaneously evaluate the solution of the fourth order ODEs at individual grid points in a self-starting mode. The basic properties of the implicit block method are investigated, and the block method is seen to satisfy the property of convergence which is displayed in the numerical results obtained. Furthermore, in comparison to works of past authors the implicit block method gives more impressive results.
In view of the fact that block methods are adequate to numerically approximate second order ordinary differential equations, which can be developed with or without the presence of higher derivatives, although still possessing the same... more
In view of the fact that block methods are adequate to numerically approximate second order ordinary differential equations, which can be developed with or without the presence of higher derivatives, although still possessing the same order, we introduce block methods of equal order with and without the presence of higher derivatives using the linear block approach. The resulting block methods are employed to solve the second order ordinary differential equations. The accuracy of the block methods is investigated with respect to their absolute error. It is found that the block method with the presence of higher derivative has better accuracy.
The diversity of adopting different step by step approach when developing block methods of the form A⁰Yn+k = AⁱYn-k +BⁱY•n-k +DⁱY• +h³(C⁰Y•n+k+CⁱY•n-k) is quite rigorous. Hence, this study presents an approach called Linear Block Method... more
The diversity of adopting different step by step approach when developing block methods of the form A⁰Yn+k = AⁱYn-k +BⁱY•n-k +DⁱY• +h³(C⁰Y•n+k+CⁱY•n-k) is quite rigorous. Hence, this study presents an approach called Linear Block Method (LBM) capable of producing directly any k steplength value of block methods for solving third order ordinary differential equations. The LBM algorithm is validated by recovering certain existing k-step block methods in literature. Likewise, the computational complexity of the LBM algorithm is presented.
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This study presents three approaches for developing block methods for solving second order ODEs. These approaches include the conventional numerical integration and collocation approaches while in addition, considering a new approach... more
This study presents three approaches for developing block methods for solving second order ODEs. These approaches include the conventional numerical integration and collocation approaches while in addition, considering a new approach called the linear block approach. A sample two-step block method is developed using the two conventional approaches and from the general form taken by the resulting block method, the linear block approach is adopted to directly obtain the block method. To investigate the rigour involved in adopted these approaches, the computational complexity analysis is investigated and it is observed that the new linear block approach is most suitable for developing block methods.
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This article presents a new generalized algorithm for developing k-step 1 derivative block methods for solving order ordinary differential equations. This new algorithm utilizes the concept from the conventional Taylor series approach of... more
This article presents a new generalized algorithm for developing k-step 1 derivative block methods for solving order ordinary differential equations. This new algorithm utilizes the concept from the conventional Taylor series approach of developing linear multistep methods. Certain examples are given to show the simplicity involved in the usage of this new generalized algorithm.
Third order initial value problems are generally solved numerically by developing numerical methods designed for third order differential equations. Also, to improve the accu- racy of the methods, most of the numerical methods are... more
Third order initial value problems are generally solved numerically by developing numerical methods designed for third order differential equations. Also, to improve the accu- racy of the methods, most of the numerical methods are implemented with starting values. However, it has been observed that a third derivative method developed for solving second order initial value problems can also be adopted to solve third order initial value problems. Although, this third derivative method is adopted in self-starting mode, it is seen to be very relevant from the results obtained in this paper. This third derivative block method is adopted to solve some special third order numerical problems previously solved in literature and the method gave better results despite that the previous methods have equal and higher order.
Nonlinear boundary value problems (BVPs) are more tedious to solve than their linear counterparts. This is observed in the extra computation required when determining the missing conditions in transforming BVPs to initial value problems.... more
Nonlinear boundary value problems (BVPs) are more tedious to solve than their linear counterparts. This is observed in the
extra computation required when determining the missing conditions in transforming BVPs to initial value problems. Although a
number of numerical approaches are already existent in literature to solve nonlinear BVPs, this article presents a new block method
with improved accuracy to solve nonlinear BVPs. A (𝑚 + 1)th-step block method is developed using a modified Taylor series
approach to directly solve fourth-order nonlinear boundary value problems (BVPs) where𝑚is the order of the differential equation
under consideration. The schemes obtained were combined to simultaneously produce solution to the fourth-order nonlinear BVPs
at 𝑚 + 1 points iteratively. The derived block method showed improved accuracy in comparison to previously existing authors
when solving the same problems. In addition, the suitability of the (𝑚 + 1)th-step block method was displayed in the solution for
magnetohydrodynamic squeezing flow in porous medium.
extra computation required when determining the missing conditions in transforming BVPs to initial value problems. Although a
number of numerical approaches are already existent in literature to solve nonlinear BVPs, this article presents a new block method
with improved accuracy to solve nonlinear BVPs. A (𝑚 + 1)th-step block method is developed using a modified Taylor series
approach to directly solve fourth-order nonlinear boundary value problems (BVPs) where𝑚is the order of the differential equation
under consideration. The schemes obtained were combined to simultaneously produce solution to the fourth-order nonlinear BVPs
at 𝑚 + 1 points iteratively. The derived block method showed improved accuracy in comparison to previously existing authors
when solving the same problems. In addition, the suitability of the (𝑚 + 1)th-step block method was displayed in the solution for
magnetohydrodynamic squeezing flow in porous medium.
Block methods for the numerical solution of ordinary differential equations (ODEs) are quite prominent in recent literature and second order initial value problems (IVPs) which falls in the family of ODEs is also a well explored area for... more
Block methods for the numerical solution of ordinary differential equations (ODEs) are quite prominent in recent literature and second order initial value problems (IVPs) which falls in the family of ODEs is also a well explored area for the application of block methods. The introduction of hybrid block method methods for the solution of second order IVPs has gained good grounds in literature as the presence of off grid points in the block method has increased the accuracy of the hybrid block methods. However, recent studies still continue to introduce new block methods that will perform more favourably than previously existing when compared in terms of error. Hence, a hybrid block method of order six is presented in this article to compete with previously existing methods of the same order and higher order. The methodology adopted in this article presents a new approach for developing the hybrid block method which is simple to implement and less computationally tiresome. The numerical results show this new 4-step 5-point hybrid block method performing better than previously existing methods.
Numerov method is one of the most widely used algorithms in physics and engineering for solving second order ordinary differential equations. The numerical solution of this method has been improved by different authors by using different... more
Numerov method is one of the most widely used algorithms in physics and engineering for solving second order ordinary differential equations. The numerical solution of this method has been improved by different authors by using different starting formulas but in recent years, there has been a dearth in that trend which informed the introduction of a two-step third-derivative block method in this paper to start Numerov method with the aim of getting better results than previous approaches. The selection of the steplength as two is to have a uniform basis for comparison with other existing two-step starting formula in literature. Although, the accuracy of the two-step method adopted in this article was enhanced by the introduction of higher derivative. Hence, this paper presents a two-step third-derivative block method which displayed better accuracy when adopted for starting Numerov method as shown in the numerical results. Thus, the third-derivative block method, as a starting formula, is seen to be quite suitable for starting Numerov method when applied to physical models.
In this article, a hybrid block method is utilized for the numerical approximation of second order Initial Value Problems (IVPs). The rigor of reduction to a system of first order initial value problems is bypassed as the hybrid block... more
In this article, a hybrid block method is utilized for the numerical approximation of second order Initial Value Problems (IVPs). The rigor of reduction to a system of first order initial value problems is bypassed as the hybrid block method directly solves the second order IVPs. Likewise, the methodology utilized also avoids the cumbersome steps involved in the widely adopted interpolation approach for developing hybrid block methods as a simple and easy to implement algorithm using the knowledge from the conventional Taylor series expansions with less cumbersome steps is introduced. To further justify the usability of this hybrid block method, the basic properties which will infer convergence when adopted to solve differential equations are investigated. The hybrid block method validates its superiority over existing methods as seen in the improved accuracy when solving the considered numerical examples.
Block methods have been seen to be an adequate numerical method for finding the approximate solution to second order ordinary differential equations. Thus, this article presents a block method of maximal order for the direct solution of... more
Block methods have been seen to be an adequate numerical method for finding the approximate solution to second order ordinary differential equations. Thus, this article presents a block method of maximal order for the direct solution of second order initial and boundary value problems. Taylor series expansion approach is adopted for the derivation of the block methods. From the numerical results obtained, this new block method performs better than previous numerical methods in existence in terms of accuracy, when compared to the exact solution of the numerical problems considered.
A number of authors have considered the solution of second order initial value problems (IVPs) and the adoption of block methods of order eight has been seen to be widely applied. However, these previously developed block methods have... more
A number of authors have considered the solution of second order initial value problems (IVPs) and the adoption of block methods of order eight has been seen to be widely applied. However, these previously developed block methods have considered non-hybrid grid points. Hence, this article presents a new hybrid block method of order eight for solving second order IVPs with an improved level of accuracy when compared to previously existing order eight block methods in terms of error. The methodology employed involves a new generalized algorithm for developing the hybrid block method which is another novel contribution existing in this work. Hence, not only this article presents a new block method that can be adopted when solving real life problems modelled as second order IVPs, it also gives a more convenient algorithm for developing hybrid block methods.