Spectral homotopy analysis method and composite Chebyshev finite difference method for solving integro-differential equations

In this thesis, spectral homotopy analysis method (SHAM) is proposed for solving different type of second order integro-differential equations such as linear and nonlinear Volterra, Fredholm and Volterra-Fredholm integrodifferential equations. Linear and nonlinear systems of second order Fredholm...

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Main Author:	Atabakan, Zohreh Pashazadeh
Format:	Thesis
Language:	English
Published:	2015
Subjects:	Homotopy theory Mathematical analysis
Online Access:	http://psasir.upm.edu.my/id/eprint/91919/1/FS%202015%2091%20-%20IR.pdf
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id	my-upm-ir.91919
record_format	uketd_dc
spelling	my-upm-ir.919192022-02-28T08:26:39Z Spectral homotopy analysis method and composite Chebyshev finite difference method for solving integro-differential equations 2015-03 Atabakan, Zohreh Pashazadeh In this thesis, spectral homotopy analysis method (SHAM) is proposed for solving different type of second order integro-differential equations such as linear and nonlinear Volterra, Fredholm and Volterra-Fredholm integrodifferential equations. Linear and nonlinear systems of second order Fredholm integro-differential equations are solved using SHAM. In this method, the Chebyshev pseudo spectral method is used to solve the linear high-order deformation equations. The convergence analysis of the proposed method is proved, the error estimation of the method is done and the rate of convergence is obtained. Many different examples are solved using spectral homotopy analysis method to confirm the accuracy and the efficiency of the introduced method. An efficient and accurate method based on hybrid of block-pulse functions and Chebyshev polynomials using Chebyshev-Gauss-Lobatto points is introduced for solving linear and nonlinear Fredholm and system of Fredholm integro-differential equations. The useful properties of Chebyshev polynomials and finite difference method make it a computationally efficient method to approximate the solution of Fredholm integro-differential equations. In this method, the given problem is converted into a system of algebraic equations using collocation points. The error bound of the method is estimated. Several numerical examples have been provided and compared with well-known approaches and exact solutions to confirm that the introduced method is more accurate and efficient. For future studies, some problems are proposed at the end of this thesis. Homotopy theory Differential equations, Nonlinear Mathematical analysis 2015-03 Thesis http://psasir.upm.edu.my/id/eprint/91919/ http://psasir.upm.edu.my/id/eprint/91919/1/FS%202015%2091%20-%20IR.pdf text en public doctoral Universiti Putra Malaysia Homotopy theory Differential equations, Nonlinear Mathematical analysis Kilicman, Adem
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
advisor	Kilicman, Adem
topic	Homotopy theory Homotopy theory Mathematical analysis
spellingShingle	Homotopy theory Homotopy theory Mathematical analysis Atabakan, Zohreh Pashazadeh Spectral homotopy analysis method and composite Chebyshev finite difference method for solving integro-differential equations
description	In this thesis, spectral homotopy analysis method (SHAM) is proposed for solving different type of second order integro-differential equations such as linear and nonlinear Volterra, Fredholm and Volterra-Fredholm integrodifferential equations. Linear and nonlinear systems of second order Fredholm integro-differential equations are solved using SHAM. In this method, the Chebyshev pseudo spectral method is used to solve the linear high-order deformation equations. The convergence analysis of the proposed method is proved, the error estimation of the method is done and the rate of convergence is obtained. Many different examples are solved using spectral homotopy analysis method to confirm the accuracy and the efficiency of the introduced method. An efficient and accurate method based on hybrid of block-pulse functions and Chebyshev polynomials using Chebyshev-Gauss-Lobatto points is introduced for solving linear and nonlinear Fredholm and system of Fredholm integro-differential equations. The useful properties of Chebyshev polynomials and finite difference method make it a computationally efficient method to approximate the solution of Fredholm integro-differential equations. In this method, the given problem is converted into a system of algebraic equations using collocation points. The error bound of the method is estimated. Several numerical examples have been provided and compared with well-known approaches and exact solutions to confirm that the introduced method is more accurate and efficient. For future studies, some problems are proposed at the end of this thesis.
format	Thesis
qualification_level	Doctorate
author	Atabakan, Zohreh Pashazadeh
author_facet	Atabakan, Zohreh Pashazadeh
author_sort	Atabakan, Zohreh Pashazadeh
title	Spectral homotopy analysis method and composite Chebyshev finite difference method for solving integro-differential equations
title_short	Spectral homotopy analysis method and composite Chebyshev finite difference method for solving integro-differential equations
title_full	Spectral homotopy analysis method and composite Chebyshev finite difference method for solving integro-differential equations
title_fullStr	Spectral homotopy analysis method and composite Chebyshev finite difference method for solving integro-differential equations
title_full_unstemmed	Spectral homotopy analysis method and composite Chebyshev finite difference method for solving integro-differential equations
title_sort	spectral homotopy analysis method and composite chebyshev finite difference method for solving integro-differential equations
granting_institution	Universiti Putra Malaysia
publishDate	2015
url	http://psasir.upm.edu.my/id/eprint/91919/1/FS%202015%2091%20-%20IR.pdf
_version_	1747813693510385664

Spectral homotopy analysis method and composite Chebyshev finite difference method for solving integro-differential equations

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