Journal of Amasya University the Institute of Sciences and Technology
Conventionally, the method of solving fourth order initial value problems of ordinary differentia... more Conventionally, the method of solving fourth order initial value problems of ordinary differential is to first reduce it to a system of first order differential equation. This approach affects the effectiveness and convergence of the numerical method as a result of the transformation. This paper comprises of the derivation, analysis and implementation of a new hybrid block method which is derived by collocation and interpolation of an assumed basis function. The basic properties of the block method including zero stability, error constants, consistency, order and convergence were analyzed. From the analysis, the block method derived was found to be zero stable, consistent, and convergent. Also, the block method was tested on some numerical examples and the result computed shows that the derived schemes are more accurate than existing methods in literature.
Conventionally, the method of solving fourth-order initial value problems of an ordinary differen... more Conventionally, the method of solving fourth-order initial value problems of an ordinary differential is to first reduce it to a system of first-order differential equations. This approach affects the effectiveness and convergence of the numerical method as a result of the transformation. This paper comprises of the derivation, analysis, and implementation of a new hybrid block method which is derived by collocation and interpolation of an assumed basis function. The basic properties of the block method including zero stability, error constants, consistency, order, and convergence were analyzed. From the analysis, the block method derived was found to be zero-stable, consistent, and convergent. Also, the block method was tested on some numerical examples and the result computed shows that the derived schemes are more accurate than existing methods in the literature.
Journal of Science, Technology, Mathematics and Education (JOSTMED), 2021
Plug flow can significantly enhance heat transfer in micro-channels as compared to single-phase f... more Plug flow can significantly enhance heat transfer in micro-channels as compared to single-phase flow. We investigate the impact of Peclet number and heat transfer coefficient on heat transfer in a liquid plug, solve the incompressible Newtonian fluid with constant properties and heat source, and solve the energy conservation equation by introducing a new space variable to provide an analytical solution to the two-dimensional heat transfer in the liquid plug. The governing equation was analytically handled utilizing Eigenfunction expansion techniques, which produced graphical summaries of the system responses on heat transfer, as well as the effect of Peclet number and heat transfer coefficient. The findings showed that as the Peclet number rises, so does the maximum temperature, and the temperature rises over time.
Journal of Amasya University the Institute of Sciences and Technology
Conventionally, the method of solving fourth order initial value problems of ordinary differentia... more Conventionally, the method of solving fourth order initial value problems of ordinary differential is to first reduce it to a system of first order differential equation. This approach affects the effectiveness and convergence of the numerical method as a result of the transformation. This paper comprises of the derivation, analysis and implementation of a new hybrid block method which is derived by collocation and interpolation of an assumed basis function. The basic properties of the block method including zero stability, error constants, consistency, order and convergence were analyzed. From the analysis, the block method derived was found to be zero stable, consistent, and convergent. Also, the block method was tested on some numerical examples and the result computed shows that the derived schemes are more accurate than existing methods in literature.
Conventionally, the method of solving fourth-order initial value problems of an ordinary differen... more Conventionally, the method of solving fourth-order initial value problems of an ordinary differential is to first reduce it to a system of first-order differential equations. This approach affects the effectiveness and convergence of the numerical method as a result of the transformation. This paper comprises of the derivation, analysis, and implementation of a new hybrid block method which is derived by collocation and interpolation of an assumed basis function. The basic properties of the block method including zero stability, error constants, consistency, order, and convergence were analyzed. From the analysis, the block method derived was found to be zero-stable, consistent, and convergent. Also, the block method was tested on some numerical examples and the result computed shows that the derived schemes are more accurate than existing methods in the literature.
Journal of Science, Technology, Mathematics and Education (JOSTMED), 2021
Plug flow can significantly enhance heat transfer in micro-channels as compared to single-phase f... more Plug flow can significantly enhance heat transfer in micro-channels as compared to single-phase flow. We investigate the impact of Peclet number and heat transfer coefficient on heat transfer in a liquid plug, solve the incompressible Newtonian fluid with constant properties and heat source, and solve the energy conservation equation by introducing a new space variable to provide an analytical solution to the two-dimensional heat transfer in the liquid plug. The governing equation was analytically handled utilizing Eigenfunction expansion techniques, which produced graphical summaries of the system responses on heat transfer, as well as the effect of Peclet number and heat transfer coefficient. The findings showed that as the Peclet number rises, so does the maximum temperature, and the temperature rises over time.
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