Solving delay differential equations by Runge-Kutta method using different types of interpolation

Introduction to delay differential equations (DDEs) and the areas where they arise are given. Analysis of specific numerical methods for solving delay differential equation is considered. A brief discussion on Runge-Kutta method when adapted to delay differential equation is introduced. Embedded...

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Bibliographic Details
Main Author:	Alkhasawneh, Rae'd Ali Ahmed
Format:	Thesis
Language:	English English
Published:	2001
Subjects:	Delay differential equations - Numerical solutions Runge-Kutta formulas Interpolation
Online Access:	http://psasir.upm.edu.my/id/eprint/9237/1/FSAS_2001_17.pdf
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id	my-upm-ir.9237
record_format	uketd_dc
spelling	my-upm-ir.92372024-02-13T02:48:00Z Solving delay differential equations by Runge-Kutta method using different types of interpolation 2001-12 Alkhasawneh, Rae'd Ali Ahmed Introduction to delay differential equations (DDEs) and the areas where they arise are given. Analysis of specific numerical methods for solving delay differential equation is considered. A brief discussion on Runge-Kutta method when adapted to delay differential equation is introduced. Embedded Singly Diagonally Implicit Runge-Kutta (SDIRK) method of third order four-stage in fourth order five-stage which is more attractive from the practical point of view is used to solve delay differential equations. The delay term is approximated using three types of interpolation that is the divided difference interpolation, Hermite interpolation and In't Hout interpolation. Numerical results based on these three interpolations are tabulated and compared. Finally, the stability properties of SDIRK method when applied to DDEs using Lagrange interpolation and In't Hout interpolation are investigated and their regions of stability are presented. Delay differential equations - Numerical solutions Runge-Kutta formulas Interpolation 2001-12 Thesis http://psasir.upm.edu.my/id/eprint/9237/ http://psasir.upm.edu.my/id/eprint/9237/1/FSAS_2001_17.pdf text en public masters Universiti Putra Malaysia Delay differential equations - Numerical solutions Runge-Kutta formulas Interpolation Faculty of Science and Environmental Studies Ismail, Fudziah English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
advisor	Ismail, Fudziah
topic	Delay differential equations - Numerical solutions Runge-Kutta formulas Interpolation
spellingShingle	Delay differential equations - Numerical solutions Runge-Kutta formulas Interpolation Alkhasawneh, Rae'd Ali Ahmed Solving delay differential equations by Runge-Kutta method using different types of interpolation
description	Introduction to delay differential equations (DDEs) and the areas where they arise are given. Analysis of specific numerical methods for solving delay differential equation is considered. A brief discussion on Runge-Kutta method when adapted to delay differential equation is introduced. Embedded Singly Diagonally Implicit Runge-Kutta (SDIRK) method of third order four-stage in fourth order five-stage which is more attractive from the practical point of view is used to solve delay differential equations. The delay term is approximated using three types of interpolation that is the divided difference interpolation, Hermite interpolation and In't Hout interpolation. Numerical results based on these three interpolations are tabulated and compared. Finally, the stability properties of SDIRK method when applied to DDEs using Lagrange interpolation and In't Hout interpolation are investigated and their regions of stability are presented.
format	Thesis
qualification_level	Master's degree
author	Alkhasawneh, Rae'd Ali Ahmed
author_facet	Alkhasawneh, Rae'd Ali Ahmed
author_sort	Alkhasawneh, Rae'd Ali Ahmed
title	Solving delay differential equations by Runge-Kutta method using different types of interpolation
title_short	Solving delay differential equations by Runge-Kutta method using different types of interpolation
title_full	Solving delay differential equations by Runge-Kutta method using different types of interpolation
title_fullStr	Solving delay differential equations by Runge-Kutta method using different types of interpolation
title_full_unstemmed	Solving delay differential equations by Runge-Kutta method using different types of interpolation
title_sort	solving delay differential equations by runge-kutta method using different types of interpolation
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science and Environmental Studies
publishDate	2001
url	http://psasir.upm.edu.my/id/eprint/9237/1/FSAS_2001_17.pdf
_version_	1794018807411376128

Solving delay differential equations by Runge-Kutta method using different types of interpolation

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