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

Authors : Muideen OGUNNİRAN, Abdulraouv ALABİ, Qasim AMOBİ, Sabastine EMMANUEL

Pages : 50-60

View : 15 | Download : 11

Publication Date : 2021-09-30

Article Type : Research Paper

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 $u``insert ignore into journalissuearticles values(t);$ 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