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Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method

The solution of higher-index Hessenberg differential-algebraic equations (DAEs) is of great importance since this type of DAEs often arises in applications. Higher-index DAEs are known to be numerically and analytically difficult to solve. In this paper, we present a new analytical method for the so...

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Autor principal: Benhammouda, Brahim
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4628135/
https://www.ncbi.nlm.nih.gov/pubmed/26543782
http://dx.doi.org/10.1186/s40064-015-1443-3
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author Benhammouda, Brahim
author_facet Benhammouda, Brahim
author_sort Benhammouda, Brahim
collection PubMed
description The solution of higher-index Hessenberg differential-algebraic equations (DAEs) is of great importance since this type of DAEs often arises in applications. Higher-index DAEs are known to be numerically and analytically difficult to solve. In this paper, we present a new analytical method for the solution of two classes of higher-index Hessenberg DAEs. The method is based on Adomian polynomials and the differential transform method (DTM). First, the DTM is applied to the DAE where the differential transforms of nonlinear terms are calculated using Adomian polynomials. Then, based on the index condition, the resulting recursion system is transformed into a nonsingular linear algebraic system. This system is then solved to obtain the coefficients of the power series solution. The main advantage of the proposed technique is that it does not require an index reduction nor a linearization. Two test problems are solved to demonstrate the effectiveness of the method. In addition, to extend the domain of convergence of the approximate series solution, we propose a post-treatment with Laplace-Padé resummation method.
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spelling pubmed-46281352015-11-05 Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method Benhammouda, Brahim Springerplus Research The solution of higher-index Hessenberg differential-algebraic equations (DAEs) is of great importance since this type of DAEs often arises in applications. Higher-index DAEs are known to be numerically and analytically difficult to solve. In this paper, we present a new analytical method for the solution of two classes of higher-index Hessenberg DAEs. The method is based on Adomian polynomials and the differential transform method (DTM). First, the DTM is applied to the DAE where the differential transforms of nonlinear terms are calculated using Adomian polynomials. Then, based on the index condition, the resulting recursion system is transformed into a nonsingular linear algebraic system. This system is then solved to obtain the coefficients of the power series solution. The main advantage of the proposed technique is that it does not require an index reduction nor a linearization. Two test problems are solved to demonstrate the effectiveness of the method. In addition, to extend the domain of convergence of the approximate series solution, we propose a post-treatment with Laplace-Padé resummation method. Springer International Publishing 2015-10-29 /pmc/articles/PMC4628135/ /pubmed/26543782 http://dx.doi.org/10.1186/s40064-015-1443-3 Text en © Benhammouda. 2015 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Benhammouda, Brahim
Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method
title Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method
title_full Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method
title_fullStr Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method
title_full_unstemmed Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method
title_short Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method
title_sort solution of nonlinear higher-index hessenberg daes by adomian polynomials and differential transform method
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4628135/
https://www.ncbi.nlm.nih.gov/pubmed/26543782
http://dx.doi.org/10.1186/s40064-015-1443-3
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