Thesis-1998-Mokhtarzadeh.pdf (3.24 MB)
A general global approximation method for the solution of boundary value problems
thesis
posted on 2014-04-14, 14:00 authored by M.R. MokhtarzadehA general global approximation scheme is developed and its generality is
demonstrated by the derivation of classical Lagrange and Hermite interpolation
and finite difference and finite element approximations as its special
cases. It is also shown that previously reported general approximation techniques
which use the idea of moving least square are also special cases of
the present method. The combination of the developed general global approximation
technique with the weighted residual methods provides a very
powerful scheme for the solution of the boundary value problems formulated
in terms of differential equations. Although this application is the main
purpose of the this project, nevertheless, the power and flexibility of the developed
approximation allows it to be used in many other areas. In this study
the following applications of the described approximation are developed:
1- data fitting (including curve and surface fitting)
2- plane mapping (both in cases where a conformal mapping exists and for
non-conformal mapping)
3- solution of eigenvalue problems with particular application to spectral expansions
used in the modal representation of shallow water equations
4- solution of ordinary differential equations (including Sturm-Liouville equations,
non-homogeneous equations with non-smooth right hand sides and 4th
order equations)
5- elliptic partial differential equations (including Poisson equations with
non-smooth right hand sides)
A computer program which can handle the above applications is developed.
This program utilises symbolic, numerical and graphical and the programming
language provided by the Mathematica package.
History
School
- Aeronautical, Automotive, Chemical and Materials Engineering
Department
- Chemical Engineering
Publisher
© M.R.MokhtarzadehPublication date
1998Notes
A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Engineering of Loughborough UniversityEThOS Persistent ID
uk.bl.ethos.289634Language
- en