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. [ABSTRACT FROM AUTHOR]