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)
The main aim of this paper intends to discuss the solution of general dual fuzzy linear system (GDFLS) C BX F AX + = + where A , B are real n m × matrix , F and C are fuzzy vectors, and the unknown vector X is a vector consisting of n fuzzy numbers, by a special algorithm based on a class of ABS algorithms called Huang algorithm. In special case, we apply… (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.
The main aim of this paper intends to discuss the solution of fuzzy Sylvester matrix equation AX + XB = C where A = (a ij) ∈ R n×n , B = (b ij) ∈ R m×m are crisp M-matrices, C = (c ij) ∈ R n×m is fuzzy matrix and X ∈ R n×m is unknown,by applying a special algorithm based on a class of ABS algorithms called Huang algorithm. At first, we transform this system… (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)