Modified Reduced Differential Transform Method for Partial Differential-Algebraic Equations

This work presents the application of the reduced differential transform method (RDTM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-two and index-three are solved to show that RDTM can provide analytical solutions for PDAEs in convergent series form. In addition, we present the posttreatment of the power series solutions with the Laplace-Padé resummation method as a useful technique to find exact solutions. The main advantage of the proposed technique is that it is based on a few straightforward steps and does not generate secular terms or depend on a perturbation parameter.