Solution of the differential algebraic equations via homotopy perturbation method and their engineering applications

Abstract

Differential algebraic equations (DAEs) appear in many fields of physics and have a wide range of applications in various branches of science and engineering. Finding reliable methods to solve DAEs has been the subject of many investigations in recent years. In this paper, the He's homotopy perturbation method is applied for finding the solution of linear and nonlinear DAEs. First, an index reduction technique is implemented for semi-explicit and Hessenberg DAEs, then the obtained problem can be appropriately solved by the homotopy perturbation method. This technique provides a summation of an infinite series with easily computable terms, which converges to the exact solution of the problem. The scheme is tested for some high-index DAEs and the results demonstrate that the method is very straightforward and can be considered as a powerful mathematical tool.