Computational approaches to initial-boundary value problems with Neumann boundary conditions

Abstract

In this paper, recursive solution schemes for different boundary value problems and initial-boundary value problems of partial differential equations with Neumann boundary conditions are proposed. The schemes are based on the Lesnic's approach and the Advanced Adomian decomposition method (AADM). The Lesnic's approach to homogeneous and inhomogeneous initial-boundary value problems was generalized. Also, the AADM to initial-boundary value problems was extended. Some examples were presented to demonstrate the high accuracy and efficiency of the proposed schemes.

Keywords

• Advanced Adomian decomposition method
• Lesnic's approach
• Neumann boundary conditions
• initial-boundary value problem