Fourth Derivative Block Method for Solving Two-point Singular Boundary Value Problems and Related Stiff Problems

Year 2021, Volume: 6 Issue: 2, 50 - 60, 30.09.2021

Muideen Ogunniran , Abdulraouv Alabi Qasim Amobi Sabastine Emmanuel

https://izlik.org/JA46GZ83JA

Abstract

This paper contains the formulation of an algorithm for solving two-point singular nonlinear boundary value problems of ordinary differential equations. This method is basically a fourth derivative block method obtained from the collocation and interpolation of an assumed derivatives and functional of a basis function. Its implementation was on the evaluation of derivatives of the given smooth first derivative function $u''(t)$ up to the fourth derivative, at some points $t$. It is proved that the algorithm is consistent, zero-stable and convergent. Errors for uniform step lengths are also investigated. Numerical examples are provided to show the efficiency of the algorithm.

Keywords

Singular boundary value problems , Derivative methods , Block method , Linear stability , Errors

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