The effect of Darcy dissipation on melting from a vertical plate with variable temperature embedd... more The effect of Darcy dissipation on melting from a vertical plate with variable temperature embedded in porous medium is numerically studied. The partial differential equations governing the problem under consideration have been transformed by a similarity transformation into a system of ordinary differential equation which is solved numerically by Runge-Kutta-Gill methods. Dimensionless velocity, Temperature and concentration profiles are presented graphically for various values of physical parameter. During the course of integration, it is found that Increasing the values of melting result into the decrease in local nusselt number.
A Linear Multistep Hybrid Method (LMHM) with continuous coefficients is considered and directly a... more A Linear Multistep Hybrid Method (LMHM) with continuous coefficients is considered and directly applied to solve third order Initial Value Problems (IVPs). The continuous method is used to obtain Multiple Finite Difference Methods (MFDMs) each of order 5 which are combined as simultaneous numerical integrators to provide a direct solution to IVPs over sub-intervals which do not overlap. The convergence of the MFDMs is discussed by conveniently representing the MFDMs as a block method and verifying that the block method is zero-stable and consistent. The superiority of the MFDMs over the existing methods is established numerically.
The study aims to develop the theory of numerical methods used for the numerical solution of seco... more The study aims to develop the theory of numerical methods used for the numerical solution of second order ordinary differential equations (ODEs). The method is derived by the interpolation and collocation of the assumed approximate solution and its second derivative at
In this paper, we propose a class implicit six step Hybrid Backward Differentiation Formulas (HBD... more In this paper, we propose a class implicit six step Hybrid Backward Differentiation Formulas (HBDF) for the solution of second order Initial Value Problems (IVPs). The method is derived by the interpolation and collocation of the assumed approximate solution. The single continuous formulation derived is evaluated at grid point of and its second derivative at
This work is focused on the examination of the effect of thermal radiation on the heat and mass t... more This work is focused on the examination of the effect of thermal radiation on the heat and mass transfer characteristics of an incompressible electrically conducting fluid squeezed between two parallel plates in the presence of a transverse magnetic field. Using the similarity transformation, the governing system of nonlinear partial differential equations is transformed into similarity equations which are solved numerically using the Nachtsheim and Swigert shooting iteration technique together with the Runge-Kutta sixth-order integration scheme. Numerical results are presented through graphs and tables for pertinent parameters to show interesting aspects of the solution.
The Combined effect of magnetic and buoyancy forces on melting from a vertical plate having varia... more The Combined effect of magnetic and buoyancy forces on melting from a vertical plate having variable temperature embedded in porous medium are investigated numerically. The similarity equations are integrated by use of the fourth-order Runge-Kutta method coupled together with shooting techniques to satisfy the boundary conditions. The effects of Magnetic number (Ha), Melting parameter (M), Mixed convection parameter (Gr/Re) and constant (λ) on the velocity temperature profiles are presented graphically. Heat transfer in the melting region has also been studied and the effect of melting parameter and magnetic parameter on Nusselt number are presented in graphical form.
In this paper, we propose an efficient modified multistep method for direct solution of boundary ... more In this paper, we propose an efficient modified multistep method for direct solution of boundary value problems (BVPs) using multistep collocation approach. The continuous form was evaluated at grid and off-grid points to obtain the multiple finite difference schemes. The basic properties, such as order and error constants, zero stability and convergence analysis of the proposed methods were investigated. Numerical experiment were performed to show the efficiency of the method and the results were compared with the existing methods in the literature.
The direct integration of second order initial and boundary value problems is considered in this ... more The direct integration of second order initial and boundary value problems is considered in this paper. We employ a new class of orthogonal polynomials constructed as basis function to develop a two-step hybrid block method (2SHBM) adopting collocation technique. The recursive formula of the class of polynomials have been constructed, and then we give analysis of the basic properties of 2SHBM as findings show that the method is accurate and convergent. The boundary locus of the proposed 2SHBM shows that the new scheme is A-stable.
In this paper, linear multi-step hybrid block methods with three-, four-and fivestep numbers are ... more In this paper, linear multi-step hybrid block methods with three-, four-and fivestep numbers are developed for approximating directly the solution of second order Initial and Boundary Value Problems (IBVPs). Multiple finite difference formulas are derived and combined in a block formulation to form a numerical integrator that provides direct solution to second order IBVPs over sub-intervals. A new class of orthogonal polynomials constructed as basis function to develop the hybrid block methods adopting collocation technique with a non-negative weight function. The scheme is applied as simultaneous integrator to second order initial value and boundary value problems of ODEs. The properties and convergence of the proposed method are discussed. The derived schemes were used to solve some problems and the numerical result shows the effectiveness, accuracy and superiority of the method over the existing methods found in the literature.
The effect of Darcy dissipation on melting from a vertical plate with variable temperature embedd... more The effect of Darcy dissipation on melting from a vertical plate with variable temperature embedded in porous medium is numerically studied. The partial differential equations governing the problem under consideration have been transformed by a similarity transformation into a system of ordinary differential equation which is solved numerically by Runge-Kutta-Gill methods. Dimensionless velocity, Temperature and concentration profiles are presented graphically for various values of physical parameter. During the course of integration, it is found that Increasing the values of melting result into the decrease in local nusselt number.
A Linear Multistep Hybrid Method (LMHM) with continuous coefficients is considered and directly a... more A Linear Multistep Hybrid Method (LMHM) with continuous coefficients is considered and directly applied to solve third order Initial Value Problems (IVPs). The continuous method is used to obtain Multiple Finite Difference Methods (MFDMs) each of order 5 which are combined as simultaneous numerical integrators to provide a direct solution to IVPs over sub-intervals which do not overlap. The convergence of the MFDMs is discussed by conveniently representing the MFDMs as a block method and verifying that the block method is zero-stable and consistent. The superiority of the MFDMs over the existing methods is established numerically.
The study aims to develop the theory of numerical methods used for the numerical solution of seco... more The study aims to develop the theory of numerical methods used for the numerical solution of second order ordinary differential equations (ODEs). The method is derived by the interpolation and collocation of the assumed approximate solution and its second derivative at
In this paper, we propose a class implicit six step Hybrid Backward Differentiation Formulas (HBD... more In this paper, we propose a class implicit six step Hybrid Backward Differentiation Formulas (HBDF) for the solution of second order Initial Value Problems (IVPs). The method is derived by the interpolation and collocation of the assumed approximate solution. The single continuous formulation derived is evaluated at grid point of and its second derivative at
This work is focused on the examination of the effect of thermal radiation on the heat and mass t... more This work is focused on the examination of the effect of thermal radiation on the heat and mass transfer characteristics of an incompressible electrically conducting fluid squeezed between two parallel plates in the presence of a transverse magnetic field. Using the similarity transformation, the governing system of nonlinear partial differential equations is transformed into similarity equations which are solved numerically using the Nachtsheim and Swigert shooting iteration technique together with the Runge-Kutta sixth-order integration scheme. Numerical results are presented through graphs and tables for pertinent parameters to show interesting aspects of the solution.
The Combined effect of magnetic and buoyancy forces on melting from a vertical plate having varia... more The Combined effect of magnetic and buoyancy forces on melting from a vertical plate having variable temperature embedded in porous medium are investigated numerically. The similarity equations are integrated by use of the fourth-order Runge-Kutta method coupled together with shooting techniques to satisfy the boundary conditions. The effects of Magnetic number (Ha), Melting parameter (M), Mixed convection parameter (Gr/Re) and constant (λ) on the velocity temperature profiles are presented graphically. Heat transfer in the melting region has also been studied and the effect of melting parameter and magnetic parameter on Nusselt number are presented in graphical form.
In this paper, we propose an efficient modified multistep method for direct solution of boundary ... more In this paper, we propose an efficient modified multistep method for direct solution of boundary value problems (BVPs) using multistep collocation approach. The continuous form was evaluated at grid and off-grid points to obtain the multiple finite difference schemes. The basic properties, such as order and error constants, zero stability and convergence analysis of the proposed methods were investigated. Numerical experiment were performed to show the efficiency of the method and the results were compared with the existing methods in the literature.
The direct integration of second order initial and boundary value problems is considered in this ... more The direct integration of second order initial and boundary value problems is considered in this paper. We employ a new class of orthogonal polynomials constructed as basis function to develop a two-step hybrid block method (2SHBM) adopting collocation technique. The recursive formula of the class of polynomials have been constructed, and then we give analysis of the basic properties of 2SHBM as findings show that the method is accurate and convergent. The boundary locus of the proposed 2SHBM shows that the new scheme is A-stable.
In this paper, linear multi-step hybrid block methods with three-, four-and fivestep numbers are ... more In this paper, linear multi-step hybrid block methods with three-, four-and fivestep numbers are developed for approximating directly the solution of second order Initial and Boundary Value Problems (IBVPs). Multiple finite difference formulas are derived and combined in a block formulation to form a numerical integrator that provides direct solution to second order IBVPs over sub-intervals. A new class of orthogonal polynomials constructed as basis function to develop the hybrid block methods adopting collocation technique with a non-negative weight function. The scheme is applied as simultaneous integrator to second order initial value and boundary value problems of ODEs. The properties and convergence of the proposed method are discussed. The derived schemes were used to solve some problems and the numerical result shows the effectiveness, accuracy and superiority of the method over the existing methods found in the literature.
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