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Journals / Turkish Journal of Mathematics and Computer Science / 2023 / Cilt: 15 Sayı: 1

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

Nurettin DOĞAN
Hasan Hüseyin SAYAN
Pages
184–191
Publication Date
2023-06-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

So it can be applied to other DAEs.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Generally, DAEs do not have a closed form solution, so these equations have to be solved numerically.
📊
Key Findings & Data:In this work, an approximate analytic series solution of the semi-explicit DAEs is obtained by using Laplace Adomian Decomposition Method (LADM).
💡
Conclusion & Impact:So it can be applied to other DAEs.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Differential algebraic equations · index reduction · Laplace transform

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.

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Cite This Article

DOĞAN, N., SAYAN, H. H. (2023). A Novel Numerical Solution Method for Semi-explicit Differential-Algebraic Equations. Turkish Journal of Mathematics and Computer Science, Cilt: 15 Sayı: 1, 184–191. https://ajindex.com/articles/950952

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