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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
Online Access:http://psasir.upm.edu.my/id/eprint/67055/1/IPM%202016%2014%20IR.pdf
http://psasir.upm.edu.my/id/eprint/67055/
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spelling my.upm.eprints.670552019-02-18T08:23:39Z http://psasir.upm.edu.my/id/eprint/67055/ Numerical solutions of linear fredholm integro-differential equations of the second kind using quadrature-difference methods 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. 2016-12 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/67055/1/IPM%202016%2014%20IR.pdf Jalius, Chriscella (2016) Numerical solutions of linear fredholm integro-differential equations of the second kind using quadrature-difference methods. Masters thesis, Universiti Putra Malaysia.
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
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
author Jalius, Chriscella
spellingShingle Jalius, Chriscella
Numerical solutions of linear fredholm integro-differential equations of the second kind using quadrature-difference methods
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
publishDate 2016
url http://psasir.upm.edu.my/id/eprint/67055/1/IPM%202016%2014%20IR.pdf
http://psasir.upm.edu.my/id/eprint/67055/
_version_ 1643838792002437120
score 13.211869

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