The Analitical Solution of Linear and Non-Linear Differential-Algebraic Equations (DAEs) with Laplace-Padé Series Method

Abstract

In this paper, we apply Laplace-Padé Series method to solve linear and non-linear differential-algebraic equations (DAEs). Firstly, The basic properties of the Laplace-Padé Series method are given. Secondly, we calculate the arbitrary order power series of differential-algebraic equations (DAEs), then convert it to the series form Laplace-Padé. Then, the three differential-algebraic equations (DAEs) are solved by Laplace-Padé Series method. It was seen that the method gave effective and fast results. Therefore, the method can be easily applied to linear and non-linear differential-algebraic equations (DAEs) problems in different fields.