Cover Image

Solving Delay Differential Equations Using Explicit Runge-Kutta Method

Introduction to delay differential equations (DDEs) and their examples are presented. The General formulation of Explicit Runge-Kutta method when adapted to delay differential equations is described. Delay Differential Equations are solved by embedded Explicit Runge-Kutta method, which is more...

Full description

Saved in:
Bibliographic Details
Main Author: Aung, San Lwin
Format: Thesis
Language:English
English
Published: 2004
Online Access:http://psasir.upm.edu.my/id/eprint/385/1/549697_FSAS_2004_37.pdf
http://psasir.upm.edu.my/id/eprint/385/
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.upm.eprints.385
record_format eprints
spelling my.upm.eprints.3852013-05-27T06:47:59Z http://psasir.upm.edu.my/id/eprint/385/ Solving Delay Differential Equations Using Explicit Runge-Kutta Method Aung, San Lwin Introduction to delay differential equations (DDEs) and their examples are presented. The General formulation of Explicit Runge-Kutta method when adapted to delay differential equations is described. Delay Differential Equations are solved by embedded Explicit Runge-Kutta method, which is more attractive from the practical point of view. Embedding technique is used to solve DDEs not just with single delay, but with multiple delays. The technique is also used to get the local truncation error which provides a basis for choosing the next stepsize for the integration. The delay terms are approximated using three techniques of interpolation, which are the divided difference interpolation, Hermite interpolation, and continuous extensions formula of the Runge-Kutta method itself. Numerical results of tested problems based on these interpolations are presented and compared. Finally, the stability properties of Explicit Runge-Kutta method when applied to DDEs using Lagrange interpolation, Hermite interpolation and continuous extensions Runge-Kutta formula are investigated and their stability regions are illustrated 2004-08 Thesis NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/385/1/549697_FSAS_2004_37.pdf Aung, San Lwin (2004) Solving Delay Differential Equations Using Explicit Runge-Kutta Method. Masters thesis, Universiti Putra Malaysia. English
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
English
description Introduction to delay differential equations (DDEs) and their examples are presented. The General formulation of Explicit Runge-Kutta method when adapted to delay differential equations is described. Delay Differential Equations are solved by embedded Explicit Runge-Kutta method, which is more attractive from the practical point of view. Embedding technique is used to solve DDEs not just with single delay, but with multiple delays. The technique is also used to get the local truncation error which provides a basis for choosing the next stepsize for the integration. The delay terms are approximated using three techniques of interpolation, which are the divided difference interpolation, Hermite interpolation, and continuous extensions formula of the Runge-Kutta method itself. Numerical results of tested problems based on these interpolations are presented and compared. Finally, the stability properties of Explicit Runge-Kutta method when applied to DDEs using Lagrange interpolation, Hermite interpolation and continuous extensions Runge-Kutta formula are investigated and their stability regions are illustrated
format Thesis
author Aung, San Lwin
spellingShingle Aung, San Lwin
Solving Delay Differential Equations Using Explicit Runge-Kutta Method
author_facet Aung, San Lwin
author_sort Aung, San Lwin
title Solving Delay Differential Equations Using Explicit Runge-Kutta Method
title_short Solving Delay Differential Equations Using Explicit Runge-Kutta Method
title_full Solving Delay Differential Equations Using Explicit Runge-Kutta Method
title_fullStr Solving Delay Differential Equations Using Explicit Runge-Kutta Method
title_full_unstemmed Solving Delay Differential Equations Using Explicit Runge-Kutta Method
title_sort solving delay differential equations using explicit runge-kutta method
publishDate 2004
url http://psasir.upm.edu.my/id/eprint/385/1/549697_FSAS_2004_37.pdf
http://psasir.upm.edu.my/id/eprint/385/
_version_ 1643821808805216256
score 13.159267

Similar Items