On the Analytic Solution for a Steady Magnetohydrodynamic Equation

Abstract

The purpose of this study is to apply the Laplace-Adomian Decomposition Method (LADM) for obtaining the analytical and numerical solutions of a nonlinear differential equation that describes a magnetohydrodynamic (MHD) flow near the forward stagnation point of two-dimensional and axisymmetric bodies. By using this method, the similarity solutions of the problem are obtained for some typical values of the model parameters. For getting computational solutions, we combined the obtained series solutions by LADM with the Padé approximation. The method is easy to apply and gives high accurate results. The presented results through tables and figures show the efficiency and accuracy of the proposed technique.

Solution of the Two-Dimensional Second-Order Diffusion Equation With Nonlocal Boundary Condition

“…There are some similar methods, such as differential transformation method [4,5,11,12,22,23,13,20,21]. Other similar schemes can be seen in [14,15,16,17,18,19].…”

A Taylor series based method for solving a two-dimensional second-order equation

“…(1) with other methods. For solving these kinds of equations there are several methods, such as differential transformation method [2,3,6,4,12,11,7,8,10,21,22,23,24,25], Tau method [19,20] and homotopy perturbation method [13]. A new matrix formulation technique with arbitrary polynomial bases has been proposed for the numerical/analytical solution of the heat equation with nonlocal boundary condition [1] and Two matrix formulation techniques based on the shifted standard and shifted Chebyshev bases are proposed for the numerical solution of the wave equation with the non-local boundary condition [5].…”