A Novel Numerical Solution Method for Semi-explicit Differential-Algebraic Equations

Year 2023, Volume: 15 Issue: 1, 184 - 191, 30.06.2023

Nurettin Doğan , Hasan Hüseyin Sayan

Abstract

Generally, DAEs do not have a closed form solution, so these equations have to be solved numerically. In this work, an approximate analytic series solution of the semi-explicit DAEs is obtained by using Laplace Adomian Decomposition Method (LADM). Before directly solving the high-index semi-explicit DAEs, we apply the index reduction method to high-index semi-explicit DAEs since solving high-index semi-explicit DAEs is difficult. Then, we use the LADM obtaining the numerical solution. To show computational capability and efficiency of the LADM for the solution of semi-explicit DAEs, a couple of numerical examples are given. It has been shown that the intoduced algorithm has a very good accuricy compared with exact solution for the semi-explicit DAEs. So it can be applied to other DAEs.

Keywords

Differential algebraic equations , index reduction , Laplace transform , Adomian decomposition method , approximation solution

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