Solution Procedure for Systems of Partial Dierential-Algebraic Equations by NHPM and Laplace-Padé Resummation

In this paper, we propose an ecient modication of a New Homotopy Perturbation Method (NHPM) to obtain approximate and exact analytical solutions of Partial Dierential-Algebraic Equations (PDAEs). The NHPM is rst applied to the PDAE to obtain the exact solution in convergent series form. To improve the solution obtained from NHPM's truncated series, a post-treatment combining Laplace transform and Pade approximant is proposed. This modied Laplace-Pade new homotopy perturbation method is shown to be eective and greatly improves NHPM's truncated series solutions in convergence rate, and often leads to the exact solution. Two problems are solved to demonstrate the eciency of the method; the rst one is a nonlinear index-one system with an integral term and the second one is a linear index-three system with variable coecients.