Numerical Solution of Ordinary and Delay Differential Equations by Runge-Kutta Type Methods

Runge-Kutta methods for the solution of systems of ordinary differential equations (ODEs) are described. To overcome the difficulty in implementing fully implicit Runge-Kutta method and to avoid the limitations of explicit Runge-Kutta method, we resort to Singly Diagonally Implicit Runge-Kutta (S...

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Main Author:	Ismail, Fudziah
Format:	Thesis
Language:	English English
Published:	1999
Subjects:	Runge-Kutta formulas Delay differential equations - Numerical solutions
Online Access:	http://psasir.upm.edu.my/id/eprint/8653/1/FSAS_1999_5_A.pdf
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id	my-upm-ir.8653
record_format	uketd_dc
spelling	my-upm-ir.86532012-12-14T02:02:10Z Numerical Solution of Ordinary and Delay Differential Equations by Runge-Kutta Type Methods 1999 Ismail, Fudziah Runge-Kutta methods for the solution of systems of ordinary differential equations (ODEs) are described. To overcome the difficulty in implementing fully implicit Runge-Kutta method and to avoid the limitations of explicit Runge-Kutta method, we resort to Singly Diagonally Implicit Runge-Kutta (SDIRK) method, which is computationally efficient and stiffly stable. Consequently, embedded SDIRK methods of fourth order five stages in fifth order six stages are constructed. Their regions of stability are presented and numerical results of the methods are compared with the existing methods. Stiff systems of ODEs are solved using implicit formulae and require the use of Newton-like iteration, which needs a lot of computational effort. If the systems can be partitioned dynamically into stiff and nonstiff subsystems then a more effective code can be developed. Hence, partitioning strategies are discussed in detail and numerical results based on two techniques to detect stiffness using SDIRK methods are compared. A brief introduction to delay differential equations (DDEs) is given. The stability properties of SDIRK methods, when applied to DDEs, using Lagrange interpolation to evaluate the delay term, are investigated. Finally, partitioning strategies for ODEs are adapted to DDEs and numerical results based on two partitioning techniques, interval wise partitioning and componentwise partitioning are tabulated and compared. Runge-Kutta formulas Delay differential equations - Numerical solutions 1999 Thesis http://psasir.upm.edu.my/id/eprint/8653/ http://psasir.upm.edu.my/id/eprint/8653/1/FSAS_1999_5_A.pdf application/pdf en public phd doctoral Universiti Putra Malaysia Runge-Kutta formulas Delay differential equations - Numerical solutions Faculty of Environmental Studies English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Runge-Kutta formulas Delay differential equations - Numerical solutions
spellingShingle	Runge-Kutta formulas Delay differential equations - Numerical solutions Ismail, Fudziah Numerical Solution of Ordinary and Delay Differential Equations by Runge-Kutta Type Methods
description	Runge-Kutta methods for the solution of systems of ordinary differential equations (ODEs) are described. To overcome the difficulty in implementing fully implicit Runge-Kutta method and to avoid the limitations of explicit Runge-Kutta method, we resort to Singly Diagonally Implicit Runge-Kutta (SDIRK) method, which is computationally efficient and stiffly stable. Consequently, embedded SDIRK methods of fourth order five stages in fifth order six stages are constructed. Their regions of stability are presented and numerical results of the methods are compared with the existing methods. Stiff systems of ODEs are solved using implicit formulae and require the use of Newton-like iteration, which needs a lot of computational effort. If the systems can be partitioned dynamically into stiff and nonstiff subsystems then a more effective code can be developed. Hence, partitioning strategies are discussed in detail and numerical results based on two techniques to detect stiffness using SDIRK methods are compared. A brief introduction to delay differential equations (DDEs) is given. The stability properties of SDIRK methods, when applied to DDEs, using Lagrange interpolation to evaluate the delay term, are investigated. Finally, partitioning strategies for ODEs are adapted to DDEs and numerical results based on two partitioning techniques, interval wise partitioning and componentwise partitioning are tabulated and compared.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Ismail, Fudziah
author_facet	Ismail, Fudziah
author_sort	Ismail, Fudziah
title	Numerical Solution of Ordinary and Delay Differential Equations by Runge-Kutta Type Methods
title_short	Numerical Solution of Ordinary and Delay Differential Equations by Runge-Kutta Type Methods
title_full	Numerical Solution of Ordinary and Delay Differential Equations by Runge-Kutta Type Methods
title_fullStr	Numerical Solution of Ordinary and Delay Differential Equations by Runge-Kutta Type Methods
title_full_unstemmed	Numerical Solution of Ordinary and Delay Differential Equations by Runge-Kutta Type Methods
title_sort	numerical solution of ordinary and delay differential equations by runge-kutta type methods
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Environmental Studies
publishDate	1999
url	http://psasir.upm.edu.my/id/eprint/8653/1/FSAS_1999_5_A.pdf
_version_	1747810848993181696

Numerical Solution of Ordinary and Delay Differential Equations by Runge-Kutta Type Methods

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