Finite Difference Method for Numerical Solution of Two Point Boundary Value Problems with Non-uniform Mesh and Internal Boundary Condition

Finite Difference Method for Numerical Solution of Two Point Boundary Value Problems with Non-uniform Mesh and Internal Boundary Condition

Volume 4, Issue 1, Article 2 - 2018

Authors: P. K. Pandey

Copyright © 2018 . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract

In this article, we have presented a variable step finite difference method for solving second order boundary value problems in ordinary differential equations with an internal boundary condition. We have discussed the convergence and established at least cubic order of accuracy of the proposed method. The proposed method tested on several model problems for the numerical solution. The numerical results obtained for these model problems with known / constructed exact solution confirm the theoretical conclusions of the proposed method. The computational results obtained for these model problems suggest that method is efficient and accurate.

How To Cite This Article

@article{Pandey_2018, doi = {10.31559/glm2016.4.1.2}, url = {https://doi.org/10.31559%2Fglm2016.4.1.2}, year = 2018, month = {jan}, publisher = {Refaad for Studies and Research}, volume = {4}, number = {1}, author = {P. K. Pandey}, title = {Finite Difference Method for Numerical Solution of Two Point Boundary Value Problems with Non-uniform Mesh and Internal Boundary Condition}, journal = {General Letters in Mathematics} }
Pandey, P. K. (2018). Finite Difference Method for Numerical Solution of Two Point Boundary Value Problems with Non-uniform Mesh and Internal Boundary Condition. General Letters in Mathematics, 4(1). doi:10.31559/glm2016.4.1.2
[1]P. K. Pandey, “Finite Difference Method for Numerical Solution of Two Point Boundary Value Problems with Non-uniform Mesh and Internal Boundary Condition,” General Letters in Mathematics, vol. 4, no. 1, Jan. 2018.
Pandey, P. K. “Finite Difference Method for Numerical Solution of Two Point Boundary Value Problems with Non-Uniform Mesh and Internal Boundary Condition.” General Letters in Mathematics 4, no. 1 (January 1, 2018). doi:10.31559/glm2016.4.1.2.