Solving Delay Differential Equations Using Explicit Runge-Kutta Method

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...

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Main Author: Aung, San Lwin
Format: Thesis
Language:English
English
Published: 2004
Subjects:
Delay differential equations - Numerical solutions
Runge-Kutta formulas
Online Access:http://psasir.upm.edu.my/id/eprint/385/1/549697_FSAS_2004_37.pdf
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id my-upm-ir.385
record_format uketd_dc
spelling my-upm-ir.3852013-05-27T06:47:59Z Solving Delay Differential Equations Using Explicit Runge-Kutta Method 2004-08 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 Delay differential equations - Numerical solutions Runge-Kutta formulas 2004-08 Thesis http://psasir.upm.edu.my/id/eprint/385/ http://psasir.upm.edu.my/id/eprint/385/1/549697_FSAS_2004_37.pdf application/pdf en public masters Universiti Putra Malaysia Delay differential equations - Numerical solutions Runge-Kutta formulas Faculty of Environmental Studies English
institution Universiti Putra Malaysia
collection PSAS Institutional Repository
language English
English
topic Delay differential equations - Numerical solutions
Runge-Kutta formulas
spellingShingle Delay differential equations - Numerical solutions
Runge-Kutta formulas

Aung, San Lwin
Solving Delay Differential Equations Using Explicit Runge-Kutta Method
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
qualification_level Master's degree
author Aung, San Lwin
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
granting_institution Universiti Putra Malaysia
granting_department Faculty of Environmental Studies
publishDate 2004
url http://psasir.upm.edu.my/id/eprint/385/1/549697_FSAS_2004_37.pdf
_version_ 1747810209484505088

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