Adomian decomposition method by Gegenbauer and Jacobi polynomials

Abstract

In this paper, orthogonal polynomials on [–1,1] interval are used to modify the Adomian decomposition method (ADM). Gegenbauer and Jacobi polynomials are employed to improve the ADM and compared with the method of using Chebyshev and Legendre polynomials. To show the efficiency of the developed method, some linear and nonlinear examples are solved by the proposed method, results are compared with other modifications of the ADM and the exact solutions of the problems.

Keywords:

• Adomian decomposition method
• orthogonal polynomials
• Gegenbauer polynomials
• Jacobi polynomials

2000 AMS Subject Classifications :

• 33C45
• 34K28
• 34L30
• 34K06

Acknowledgements

This work is a part of the corresponding author's Ph.D. Thesis. This research is supported by Tubitak and Selcuk University Scientific Research Projects Coordinatorship.