Solving matrix differential and integro-differential equations using differential transformation method and convolutions

The differential transform method (DTM) was introduced to solve linear and nonlinear initial value problems which appear in electrical circuit analysis. In this method we construct approximate solutions which is close to the exact solutions that differentiable and having high accuracy with minor...

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Main Author:	Altun, Omer
Format:	Thesis
Language:	English
Published:	2016
Subjects:	Differential equations - Numerical solutions
Online Access:	http://psasir.upm.edu.my/id/eprint/66867/1/FS%202016%2063%20IR.pdf
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id	my-upm-ir.66867
record_format	uketd_dc
spelling	my-upm-ir.668672019-02-07T04:57:41Z Solving matrix differential and integro-differential equations using differential transformation method and convolutions 2016-09 Altun, Omer The differential transform method (DTM) was introduced to solve linear and nonlinear initial value problems which appear in electrical circuit analysis. In this method we construct approximate solutions which is close to the exact solutions that differentiable and having high accuracy with minor error. However, DTM is differ with the traditional high order Taylor series where we need long computation time and derivatives. Thus the DTM is applied to the high order differential equations as alternative way to get Taylor series solution. In final stage this method yields truncated series solution in the practical applications and most of time coincides with the Taylor expansion. In this work we study the differential equations systems by using the differential transformation method (DTM). Further, we apply the convolutions to matrices and study their fundamental properties using differential transformation method. We also provide many different applications of matrix convolutional equations such as coupled matrix convolution equations by DTM. In the applications, we proved that the solutions converge to the exact solutions. Finally we propose to generate matrix integro-differential equations by using convolutions and differential equations. Differential equations - Numerical solutions 2016-09 Thesis http://psasir.upm.edu.my/id/eprint/66867/ http://psasir.upm.edu.my/id/eprint/66867/1/FS%202016%2063%20IR.pdf text en public doctoral Universiti Putra Malaysia Differential equations - Numerical solutions
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Differential equations - Numerical solutions
spellingShingle	Differential equations - Numerical solutions Altun, Omer Solving matrix differential and integro-differential equations using differential transformation method and convolutions
description	The differential transform method (DTM) was introduced to solve linear and nonlinear initial value problems which appear in electrical circuit analysis. In this method we construct approximate solutions which is close to the exact solutions that differentiable and having high accuracy with minor error. However, DTM is differ with the traditional high order Taylor series where we need long computation time and derivatives. Thus the DTM is applied to the high order differential equations as alternative way to get Taylor series solution. In final stage this method yields truncated series solution in the practical applications and most of time coincides with the Taylor expansion. In this work we study the differential equations systems by using the differential transformation method (DTM). Further, we apply the convolutions to matrices and study their fundamental properties using differential transformation method. We also provide many different applications of matrix convolutional equations such as coupled matrix convolution equations by DTM. In the applications, we proved that the solutions converge to the exact solutions. Finally we propose to generate matrix integro-differential equations by using convolutions and differential equations.
format	Thesis
qualification_level	Doctorate
author	Altun, Omer
author_facet	Altun, Omer
author_sort	Altun, Omer
title	Solving matrix differential and integro-differential equations using differential transformation method and convolutions
title_short	Solving matrix differential and integro-differential equations using differential transformation method and convolutions
title_full	Solving matrix differential and integro-differential equations using differential transformation method and convolutions
title_fullStr	Solving matrix differential and integro-differential equations using differential transformation method and convolutions
title_full_unstemmed	Solving matrix differential and integro-differential equations using differential transformation method and convolutions
title_sort	solving matrix differential and integro-differential equations using differential transformation method and convolutions
granting_institution	Universiti Putra Malaysia
publishDate	2016
url	http://psasir.upm.edu.my/id/eprint/66867/1/FS%202016%2063%20IR.pdf
_version_	1747812419093135360

Solving matrix differential and integro-differential equations using differential transformation method and convolutions

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