Author:
Mohamed M. Khader ,Amr M. S. Mahdy
Abstract
In this article, an efficient modification of the Picard iteration method (PIM) is presented by using Chebyshev polynomials. Special attention is given to study the convergence of the proposed method. The proposed modification is tested for some examples to demonstrate reliability and efficiency of the introduced method. A comparison between our numerical results against the conventional numerical method, fourth-order Runge-Kutta method (RK4) is given. From the presented examples, we found that the proposedmethod can be applied to wide class of non-linear ordinary differential equations.
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