Thesis-1986-Sanugi.pdf (7.53 MB)
New numerical strategies for initial value type ordinary differential equations
thesis
posted on 2014-02-13, 11:19 authored by Bahrom B SanugiThis thesis is concerned with the development of new numerical
techniques for solving initial value problems in ordinary differential
equations (ODE).
The thesis begins with an introductory chapter on initial value
type problems in ordinary differential equations followed by a chapter
on basic mathematical concepts, which introduces and discusses, among
others, the theory of Arithmetic and Geometric Means. This is
followed, in Chapter 3, by a survey of the existing ODE solvers and
their theoretical background. The advantages and disadvantages of some
different strategies in terms of stability and truncation error are
also considered.
The presentation of the elementary methods based on Arithmetic
Mean (AM) and Geometric Mean (GM) formulae is done in Chapter 4, with
emphasis on establishing the GM trapezoida1 formula, and to the study
of its stability and truncation error. Applications in the predictorcorrector
and the extrapolation techniques are also considered.
Special application in the solution of delay differential equations is
also presented. .In Chapter 5, the application of the GM strategy in the Runge-Kutta
type formulae is considered, producing a new class of methods called
the GM-Runge-Kutta formulae which is found to be as competitive as the
classical Runge-Kutta methods. Thereafter, a new strategy of error
control called the Arithmeto-Geometric Mean (AGM) strategy is
developed. Further application of the GM-Runge-Kutta in Fehlberg type
formulae, and the GM-Iterative Multistep formulae are also considered. Chapter 6 concerns with further applications of GM techniques in
the development of generalised GM mu1tistep and multiderivative
methods, and for solving y'=λ(X)Y. The general idea of the GM are also
extended to other types of Means, such as Harmonic and Logarithmic
Means.
In Chapter 7, some new formulae for solving problems with
oscillatory and periodic solutions are considered.
Finally the thesis concludes with recommendations for further
work.
History
School
- Science
Department
- Computer Science
Publisher
© Bahrom Bin SanugiPublication date
1986Notes
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.EThOS Persistent ID
uk.bl.ethos.374471Language
- en