A segmented and weighted Adomian decomposition algorithm for boundary value problem of nonlinear groundwater equation

Abstract

Based on Adomian decomposition method, a new algorithm for solving boundary value problem (BVP) of nonlinear partial differential equations on the rectangular area is proposed. The solutions obtained by the method precisely satisfy all boundary conditions, except the small pieces near the four corners of the rectangular area. A theorem on the boundary error is given. Hence, the Adomian decomposition method is more efficiently applied to BVPs for partial differential equations. Segmented and weighted analytical solutions with a high accuracy for the BVP of nonlinear groundwater equations on a rectangular area are obtained by the present algorithm. Copyright © 2013 John Wiley & Sons, Ltd.

Deflection problem of circular plates of variable thickness with fixed edges under uniform loaded

“…Based on the Adomian decomposition method, Duan et al [18,19] studied systems of fractional differential equationsy and boundary value problems for higher order nonlinear differential equations; Wazwaz [20,21,22] solved the generalized Emden-Fowler equation, the higher dimensional initial boundary value problems of variable coefficients, the systems of the Volterra integral forms of the Lane-Emden equations; Zeidan et al [23] studied the solution of Burgers' equations; Gbadamosi et al [25] solved Riccati equation with variable coefficient and constant coefficient; Khater et al [26] investigated the analytical and semi-analytical solutions of the time-fractional Cahn-Allen equation. Furthermore, Patel et al [27] computed an approximate analytical solution of magneto-hydrodynamic Jeffery-Hamel flow by using a new modification of Adomian decomposition method; Yun et al [28,29,30] used Adomian decomposition method to solve the heterogeneous aquifer model on the triangular groundwater flow region; Farman et al [31] used Laplace Adomian Decomposition Method to give an approximate solution of nonlinear system of purposed model; Lisboa [32] applied a modified version of the Adomian decomposition method to nonlinear bending of laminated thick plates; Hassan [33] used the modified Adomian decomposition method investigated problem of a reactive hydromagnetic couple stress fluid flow through a saturated porous channel and so on.…”

A segmented Adomian algorithm for the boundary value problem of a second-order partial differential equation on a plane triangle area

“…Shidfar and Garshasbi [21] proposed a weighted algorithm of the ADM by combining the two partial solutions with a weight. Yun et al [22] proposed a segmented and weighted Adomian decomposition algorithm to decease the boundary error of the Adomian solution, they also presented a corresponding algorithm.…”