Two-point diagonally implicit multistep block method for solving volterra integro-differential equation of second kind

The first part of the thesis focuses on solving Volterra integro-differential equation (VIDE) of the second kind with the multistep block method. The two points diagonally implicit multistep block (2PDIB) method is formulated for the numerical solution of the second kind of VIDE. The derivatio...

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Main Author:	Baharum, Nur Auni
Format:	Thesis
Language:	English
Published:	2018
Subjects:	Volterra equations Integro-differential equations
Online Access:	http://psasir.upm.edu.my/id/eprint/69426/1/IPM%202018%205%20IR.pdf
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id	my-upm-ir.69426
record_format	uketd_dc
spelling	my-upm-ir.694262019-07-10T00:48:03Z Two-point diagonally implicit multistep block method for solving volterra integro-differential equation of second kind 2018-01 Baharum, Nur Auni The first part of the thesis focuses on solving Volterra integro-differential equation (VIDE) of the second kind with the multistep block method. The two points diagonally implicit multistep block (2PDIB) method is formulated for the numerical solution of the second kind of VIDE. The derivation of the 2PDIB method can be obtained using Lagrange interpolating polynomial. The numerical solution of the second kind of VIDE computed at two points simultaneously in block form using the proposed method using constant step size. These numerical solutions are executed in the predictor-corrector mode. Since an integral part of VIDE cannot be solved explicitly and analytically, the idea to approximate the solution of the integral part is discussed and the appropriate order of numerical integration formulae is chosen to approximate the solution of the integral part of VIDE which include trapezoidal rule, Simpson’s rule and Boole’s rule. Regarding the general form of VIDE, there are two cases of the kernel which are K(x; s) = 1 and K(x; s) ≠= 1. Two different procedures are developed to obtain the solution for these cases. The stability region is discussed based on the stability polynomial of the 2PDIB method paired with the appropriate quadrature rule. Linear and nonlinear problems of VIDE have been solved numerically using the 2PDIB method. Six tested problems are presented in order to study the performance and efficiency of the 2PDIB method in terms of maximum error, total function calls, total steps taken and the execution time taken. Numerical results showed that the efficiency of 2PDIB method when solving VIDE compared to the existing methods. Volterra equations Integro-differential equations 2018-01 Thesis http://psasir.upm.edu.my/id/eprint/69426/ http://psasir.upm.edu.my/id/eprint/69426/1/IPM%202018%205%20IR.pdf text en public masters Universiti Putra Malaysia Volterra equations Integro-differential equations
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Volterra equations Integro-differential equations
spellingShingle	Volterra equations Integro-differential equations Baharum, Nur Auni Two-point diagonally implicit multistep block method for solving volterra integro-differential equation of second kind
description	The first part of the thesis focuses on solving Volterra integro-differential equation (VIDE) of the second kind with the multistep block method. The two points diagonally implicit multistep block (2PDIB) method is formulated for the numerical solution of the second kind of VIDE. The derivation of the 2PDIB method can be obtained using Lagrange interpolating polynomial. The numerical solution of the second kind of VIDE computed at two points simultaneously in block form using the proposed method using constant step size. These numerical solutions are executed in the predictor-corrector mode. Since an integral part of VIDE cannot be solved explicitly and analytically, the idea to approximate the solution of the integral part is discussed and the appropriate order of numerical integration formulae is chosen to approximate the solution of the integral part of VIDE which include trapezoidal rule, Simpson’s rule and Boole’s rule. Regarding the general form of VIDE, there are two cases of the kernel which are K(x; s) = 1 and K(x; s) ≠= 1. Two different procedures are developed to obtain the solution for these cases. The stability region is discussed based on the stability polynomial of the 2PDIB method paired with the appropriate quadrature rule. Linear and nonlinear problems of VIDE have been solved numerically using the 2PDIB method. Six tested problems are presented in order to study the performance and efficiency of the 2PDIB method in terms of maximum error, total function calls, total steps taken and the execution time taken. Numerical results showed that the efficiency of 2PDIB method when solving VIDE compared to the existing methods.
format	Thesis
qualification_level	Master's degree
author	Baharum, Nur Auni
author_facet	Baharum, Nur Auni
author_sort	Baharum, Nur Auni
title	Two-point diagonally implicit multistep block method for solving volterra integro-differential equation of second kind
title_short	Two-point diagonally implicit multistep block method for solving volterra integro-differential equation of second kind
title_full	Two-point diagonally implicit multistep block method for solving volterra integro-differential equation of second kind
title_fullStr	Two-point diagonally implicit multistep block method for solving volterra integro-differential equation of second kind
title_full_unstemmed	Two-point diagonally implicit multistep block method for solving volterra integro-differential equation of second kind
title_sort	two-point diagonally implicit multistep block method for solving volterra integro-differential equation of second kind
granting_institution	Universiti Putra Malaysia
publishDate	2018
url	http://psasir.upm.edu.my/id/eprint/69426/1/IPM%202018%205%20IR.pdf
_version_	1747812696048271360

Two-point diagonally implicit multistep block method for solving volterra integro-differential equation of second kind

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