Numerical solutions of linear fredholm integro-differential equations of the second kind using quadrature-difference methods

Fredholm integro-differential equation (FIDE) is an equation which is the unknown functions appears under the sign of derivative and also integral sign. Therefore, the formulation of numerical quadrature rules and finite difference method are applied for solving first-order and second-order linea...

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Main Author:	Jalius, Chriscella
Format:	Thesis
Language:	English
Published:	2016
Subjects:	Differential equations - Numerical solutions Physics
Online Access:	http://psasir.upm.edu.my/id/eprint/67055/1/IPM%202016%2014%20IR.pdf
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spelling	my-upm-ir.670552019-02-18T08:23:39Z Numerical solutions of linear fredholm integro-differential equations of the second kind using quadrature-difference methods 2016-12 Jalius, Chriscella Fredholm integro-differential equation (FIDE) is an equation which is the unknown functions appears under the sign of derivative and also integral sign. Therefore, the formulation of numerical quadrature rules and finite difference method are applied for solving first-order and second-order linear FIDE of the second kind. The finite difference method is used for ordinary differential equations part, while composite quadrature rules are applied for the integral part of FIDE. Numerical solutions of linear FIDE by using quadrature-difference methods are proposed in this thesis. There are four types of formulation proposed in this thesis which are composite Simpsons 3/8 rule with first derivative of 5-point finite difference, composite Simpsons 3/8 rule with second derivative of 5-point finite difference, composite Booles rule with first derivative of 7-point finite difference and composite Booles rule with second derivative of 7-point finite difference. These formulations will be used to produce an approximation equations in order to discretize the FIDE into a system of linear algebraic equation. The system of linear algebraic equation will be solved by using Gauss elimination method. An algorithm and a coding of the proposed methods are developed in this thesis. The source of the coding for solving linear FIDE is developed by using C programming with constant step size. The four types of formulation which based on quadrature rules and finite difference method are implemented for solving Type 1 and Type 2 of first-order and secondorder linear FIDE. In this thesis, the boundary condition will be considered in solving the second-order linear FIDE. Moreover, the order of accuracy of the proposed method are studied in this thesis. Finally, the numerical experiments were carried out in order to examine the accuracy of the proposed method. The results indicated that the proposed methods are suitable for solving first-order and second-order linear FIDE of the second kind. Differential equations - Numerical solutions Physics 2016-12 Thesis http://psasir.upm.edu.my/id/eprint/67055/ http://psasir.upm.edu.my/id/eprint/67055/1/IPM%202016%2014%20IR.pdf text en public masters Universiti Putra Malaysia Differential equations - Numerical solutions Physics
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Differential equations - Numerical solutions Physics
spellingShingle	Differential equations - Numerical solutions Physics Jalius, Chriscella Numerical solutions of linear fredholm integro-differential equations of the second kind using quadrature-difference methods
description	Fredholm integro-differential equation (FIDE) is an equation which is the unknown functions appears under the sign of derivative and also integral sign. Therefore, the formulation of numerical quadrature rules and finite difference method are applied for solving first-order and second-order linear FIDE of the second kind. The finite difference method is used for ordinary differential equations part, while composite quadrature rules are applied for the integral part of FIDE. Numerical solutions of linear FIDE by using quadrature-difference methods are proposed in this thesis. There are four types of formulation proposed in this thesis which are composite Simpsons 3/8 rule with first derivative of 5-point finite difference, composite Simpsons 3/8 rule with second derivative of 5-point finite difference, composite Booles rule with first derivative of 7-point finite difference and composite Booles rule with second derivative of 7-point finite difference. These formulations will be used to produce an approximation equations in order to discretize the FIDE into a system of linear algebraic equation. The system of linear algebraic equation will be solved by using Gauss elimination method. An algorithm and a coding of the proposed methods are developed in this thesis. The source of the coding for solving linear FIDE is developed by using C programming with constant step size. The four types of formulation which based on quadrature rules and finite difference method are implemented for solving Type 1 and Type 2 of first-order and secondorder linear FIDE. In this thesis, the boundary condition will be considered in solving the second-order linear FIDE. Moreover, the order of accuracy of the proposed method are studied in this thesis. Finally, the numerical experiments were carried out in order to examine the accuracy of the proposed method. The results indicated that the proposed methods are suitable for solving first-order and second-order linear FIDE of the second kind.
format	Thesis
qualification_level	Master's degree
author	Jalius, Chriscella
author_facet	Jalius, Chriscella
author_sort	Jalius, Chriscella
title	Numerical solutions of linear fredholm integro-differential equations of the second kind using quadrature-difference methods
title_short	Numerical solutions of linear fredholm integro-differential equations of the second kind using quadrature-difference methods
title_full	Numerical solutions of linear fredholm integro-differential equations of the second kind using quadrature-difference methods
title_fullStr	Numerical solutions of linear fredholm integro-differential equations of the second kind using quadrature-difference methods
title_full_unstemmed	Numerical solutions of linear fredholm integro-differential equations of the second kind using quadrature-difference methods
title_sort	numerical solutions of linear fredholm integro-differential equations of the second kind using quadrature-difference methods
granting_institution	Universiti Putra Malaysia
publishDate	2016
url	http://psasir.upm.edu.my/id/eprint/67055/1/IPM%202016%2014%20IR.pdf
_version_	1747812436567654400

Numerical solutions of linear fredholm integro-differential equations of the second kind using quadrature-difference methods

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