In this paper, the accounting of the answers of a system of nonlinear equations is considered and a new algorithm based on the method of Adomian decomposition convergence basis for solving functional equations is presented. This algorithm is performed for some different examples and obtained results show the usage of the recommended method in this paper for… (More)
In this article, there is an attempt to introduce, generally, spectral methods for numerical solution of ordinary differential equations, also, to focus on those problems in which some coefficient functions or solution function is not analytic. Then, by expressing weak and strong aspects of spectral methods to solve this kind of problems, a modified… (More)
Here, a simple method to determine the rate of convergence of Adomian decomposition method is introduced. The proposed method is used to compare between the rate of convergence of standard and modified (proposed by Wazwaz [A.M. Wazwaz, A new method for solving singular initial value problems in the second-order ordinary differential equations, Appl. Math.… (More)
In this paper an efficient modification of the Adomian decomposition method is presented by using Chebyshev polynomials. The proposed method can be applied to linear and non-linear models. The scheme is tested for some examples and the obtained results demonstrate reliability and efficiency of the proposed method.
This paper extends an earlier work [Appl. Math. Comput. 140 (2003) 77] to differential algebraic equations with constraint singularities. Numerical solution of these problems is considered by pseudospectral method with domain decomposition and by giving a condition under which the general linear form problem can easily be transformed to the index reduced… (More)
Solutions of differential algebraic equations is considered by Adomian decomposition method. [Reducing index and spectral methods for differential-algebraic equations, J. Appl. Math. Comput. 140 (2003) 77] and M.M. Hosseini [An index reduction method for linear Hessenberg systems, J. Appl. Math. Comput., in press], an efficient technique to reduce index of… (More)
In this paper, a new iterative method for solving the system of nonlin-ear equations is suggested based on Newton-Raphson method and homotopy analysis method. Comparison of the result obtained by present method with Newton-Raphson method and homotopy perturbation method reveals that the accuracy and fast convergence of the proposed method.