An efficient modification of PIM by using Chebyshev polynomials

Mohamed M. Khadera,b,∗and Amr M. S. Mahdyc

An efficient modification of PIM by using Chebyshev polynomials

Authors :

Mohamed M. Khader^a,b,∗and Amr M. S. Mahdy^c

Author Address :

^aDepartment of Mathematics & Statistics, Faculty of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh: 11566, Saudi Arabia.
^bDepartment of Mathematics, Faculty of Science, Benha University, Benha, Egypt.
^cDepartment of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.

*Corresponding author.

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 theintroduced 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 :

Picarditeration method, Chebyshev polynomials, Runge-Kutta method, Convergence analysis.

DOI :

Article Info :

Received : July 27, 2014; Accepted : July 01, 2016.