International Journal of Nonlinear Analysis and Applications

One step hybrid block method for solving nonlinear second order Dirichlet value problems of ordinary differential equations directly

Document Type : Research Paper

Author

Department of Mathematics, College of Art and Sciences-Tabarjal, Jouf University, Saudi Arabia

Abstract

The aim of this article is to approximate the solution of nonlinear second-order Dirichlet boundary value problems of ordinary differential equations directly using the hybrid block method. To derive this method, we first transform the boundary value problem to its corresponding second-order initial value problem via the nonlinear shooting method. Then, a direct one-step hybrid block with three off-step points is derived using a collocation and interpolation approach. The numerical results clearly show that the developed method is able to generate good results when it is compared with the existing method in terms of error.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 12
December 2024
Pages 325-331
  • Receive Date: 26 September 2021
  • Revise Date: 30 September 2021
  • Accept Date: 07 December 2023