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

In this paper, we propose an efficient modification of a New Homotopy Perturbation Method (NHPM) to obtain approximate and exact analytical solutions of Partial Differential-Algebraic Equations (PDAEs). The NHPM is first 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 Padé approximant is proposed. This modified Laplace-Padé new homotopy perturbation method is shown to be effective 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 efficiency of the method; the first one is a nonlinear index-one system with an integral term and the second one is a linear index-three system with variable coefficients.