In this thesis, the two-dimensional initial and boundary value problems (IBVPs)
and the one-dimensional Cauchy problems defined by the nonlinear reaction-
diffusion and wave equations are numerically solved. The dual reciprocity boundary
element method (DRBEM) is used to discretize the IBVPs defined by single
and system of nonlinear reaction-diffusion equations and nonlinear wave equation,
spatially. The advantage of DRBEM for the exterior regions is made use
of for the latter problem. The differential quadrature method (DQM) is used
for the spatial discretization of IBVPs and Cauchy problems defined by the
nonlinear reaction-diffusion and wave equations.
The DRBEM and DQM applications result in first and second order system
of ordinary differential equations in time. These systems are solved with three
different time integration methods, the finite difference method (FDM), the least
squares method (LSM) and the finite element method (FEM) and comparisons
among the methods are made. In the FDM a relaxation parameter is used to
smooth the solution between the consecutive time levels.
It is found that DRBEM+FEM procedure gives better accuracy for the IBVPs
defined by nonlinear reaction-diffusion equation. The DRBEM+LSM procedure
with exponential and rational radial basis functions is found suitable for exterior wave problem.
The same result is also valid when DQM is used for space
discretization instead of DRBEM for Cauchy and IBVPs defined by nonlinear
reaction-diffusion and wave equations.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/3/12610568/index.pdf |
| Date | 01 May 2009 |
| Creators | Meral, Gulnihal |
| Contributors | Tezer, Munevver |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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