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

Ismail, Fudziah (1999) Numerical Solution of Ordinary and Delay Differential Equations by Runge-Kutta Type Methods. PhD thesis, Universiti Putra Malaysia.

[img] PDF
1292Kb

Abstract

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.

Item Type:Thesis (PhD)
Subject:Runge-Kutta formulas
Subject:Delay differential equations - Numerical solutions
Chairman Supervisor:Professor Mohamed bin Suleiman, PhD
Call Number:FSAS 1999 5
Faculty or Institute:Faculty of Environmental Studies
ID Code:8653
Deposited By: Nurul Hayatie Hashim
Deposited On:08 Dec 2010 08:24
Last Modified:14 Dec 2012 02:02

Repository Staff Only: Edit item detail

Document Download Statistics

This item has been downloaded for since 08 Dec 2010 08:24.

View statistics for "Numerical Solution of Ordinary and Delay Differential Equations by Runge-Kutta Type Methods"


Universiti Putra Malaysia Institutional Repository

Universiti Putra Malaysia Institutional Repository is an on-line digital archive that serves as a central collection and storage of scientific information and research at the Universiti Putra Malaysia.

Currently, the collections deposited in the IR consists of Master and PhD theses, Master and PhD Project Report, Journal Articles, Journal Bulletins, Conference Papers, UPM News, Newspaper Cuttings, Patents and Inaugural Lectures.

As the policy of the university does not permit users to view thesis in full text, access is only given to the first 24 pages only.