An efficient modification of PIM by using Chebyshev polynomials

Mohamed M. Khader; Amr M. S. Mahdy

doi:10.26637/mjm403/015

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 proposed
method can be applied to wide class of non-linear ordinary differential equations.

Keywords:

Picard iteration method, Chebyshev polynomials, Runge-Kutta method, Convergence analysis

Mathematics Subject Classification:

65N20, 41D15

Authors Imprint References Funding Related Articles Downloads

Mohamed M. Khader Department of Mathematics & Statistics, Faculty of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh: 11566, Saudi Arabia.
Amr M. S. Mahdy Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.

Pages: 453-462
Date Published: 01-07-2016
Vol. 4 No. 03 (2016): Malaya Journal of Matematik (MJM)

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