Adomian decomposition method with orthogonal polynomials: Legendre polynomials

This paper illustrates the using of orthogonal polynomials to modify the Adomian decomposition method. The method of employing Legendre polynomials to improve the Adomian decomposition method is presented here and compared to the method of using Chebyshev polynomials. The presented modified Adomian decomposition method is validated through an example and advantage as well as efficiency of this method is verified through investigating and comparing the results. In this paper, it is concluded that both orthogonal polynomials: Chebyshev and Legendre polynomials can be successfully used for the Adomian decomposition method and comparatively the Chebyshev expansion provides the better estimation.