Analytical solutions for systems of partial differential-algebraic equations

Springerplus. 2014 Mar 10:3:137. doi: 10.1186/2193-1801-3-137. eCollection 2014.

Abstract

This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.

Keywords: Laplace transform; Padé approximant; Analytical solutions; Partial differential-algebraic equations; Power series method.