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


Alkhasawneh, Rae'd Ali Ahmed (2001) Solving delay differential equations by Runge-Kutta method using different types of interpolation. Masters thesis, Universiti Putra Malaysia.


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.

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Additional Metadata

Item Type: Thesis (Masters)
Subject: Delay differential equations - Numerical solutions
Subject: Runge-Kutta formulas
Subject: Interpolation
Call Number: FSAS 2001 17
Chairman Supervisor: Fudziah bt Ismail, PhD
Divisions: Faculty of Science and Environmental Studies
Depositing User: Tuan Norasiah Tuan Yaacob
Date Deposited: 17 Jan 2011 04:06
Last Modified: 27 Sep 2013 07:30
URI: http://psasir.upm.edu.my/id/eprint/9237
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