A Numerov Type Two Phase Finite Difference Method for the Numerical Solution of the Second Order Boundary Value Problems in Ordinary Differential Equations

Year 2025, Volume: 17 Issue: 1, 296 - 303, 30.06.2025

Pramod Pandey , Archna Yadav

https://doi.org/10.47000/tjmcs.1573914

Abstract

In the present work, we propose a two-phase fourth-order method for the approximate numerical solution for second-order non-linear two-point boundary value problems with Dirichlet boundary conditions. Our numerical approach is based on a finite difference and the solution of the problem at discrete points. Our method generates a system of equations, and the solution of the system of equations is considered an approximate solution to the problem. An essential analysis of the method is considered to ensure the performance of the method. A numerical experiment is carried out with model problems to test the performance in terms of efficiency and accuracy of the proposed method.

Keywords

Finite difference method , fourth order method , modified numerov method , second order differential equation , TPBVP.

Supporting Institution

One author is getting financial support from University Grant Commission, New Delhi for this work. We are grateful to the UGC New Delhi for their support

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