Convergence and implementation of a fixed-point iterative scheme for the numerical solution of fourth-order BVPs

S.A. Khuri1, I. Louhichi, A. Sayfy

Department of Mathematics and Statistics, American University of Sharjah – UAE

Received 14 January, 2019; accepted in revised form 26 January, 2021

Abstract: In this article, we study a fixed point iteration scheme that involves the Green’s function for the numerical solution of a larger class of fourth order boundary value problems (BVPs). The scheme enjoys important features such as its high accuracy, reliability, and fast convergence. We analyze and prove convergence of the iterative procedure using the contraction principle. Several numerical examples of fourth order boundary value problems are used to test the proposed method. The numerical results clarify very good agreement with the exact solution and superiority of this approach when compared with other numerical results that exist in the literature. Furthermore, the method requires less CPU time than other techniques.

 

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