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In this paper, solving the linear and nonlinear Schrodinger equations are considered by a new numerical approach based on the homotopy analysis method (HAM). For this purpose, at first the convergence theorems of the HAM are proved to ensure that the series solution obtained from this method is able to evaluate the exact solution of the linear or nonlinear… (More)
In this article, we present a new method is presented to solve generalized Abel's fuzzy integral equations of the first kind. This method is based on the homotopy analysis method and Laplace transform method. By using this method, the accuracy and efficiency of homotopy analysis transform method (HATM) is shown. Convergence theorem of the proposed method is… (More)
In this paper, the homotopy analysis method (HAM) is applied to solve the Boussinesq equation which is a powerful method for solving the linear and nonlinear partial differential equations. For this purpose, the explicit series solution of the Boussinesq equation is obtained, then the convergence theorem is proved to illustrate the obtained series solution… (More)
In this paper, a new algorithm is presented to approximate the solution of a singularly perturbed boundary value problem with left-layer based on the homotopy perturbation technique and applying the Laplace transformation. The convergence theorem and the error bound of the proposed method are proved. The method is examined by solving two examples. The… (More)
In this paper, the convergence of Zakharov-Kuznetsov (ZK) equation by homo-topy analysis method (HAM) is investigated. A theorem is proved to guarantee the convergence of HAM and to find the series solution of this equation via a reliable algorithm.
In this paper, numerical solution of nonlinear Hammerstein integral equations via collocation method based on double exponential transformation is considered. Some remarks with respect to the computational cost and stability and implementation are discussed. Examples are presented to illustrate effectiveness of method.
—In this paper, the evaluation of I = 1 −1 f (x) √ 1−x 2 dx is proposed by using the opened and closed Gauss-Chebyshev integration rules in the stochastic arithmetic. For this purpose, a theorem is proved to show the accuracy of the Gauss-Chebyshev rules. Then, the CESTAC 1 method and the stochas-tic arithmetic are used to validate the results and implement… (More)
In this paper, we present a method for solving the second kind Singular Abel integral equation based on the discrete Gronwall inequality, Euler Maclaurin summation formula, variable transforms and modified Simpson's integration rule and Navot's quadrature. An algorithm for solving non linear weakly singular Volterra integral equations is proposed. Then, the… (More)