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Thesis
PARTIAL DIFFERENTIAL EQUATION MODELS AND THEIR NUMERICAL SOLUTIONS
University of West Florida
Master of Science (MS), University of West Florida
2015
Abstract
The purpose of this paper is to explore the nature of partial differential equation (PDE) models and numerical iterative methods to find solutions. A summary of the historical development is provided as well as a brief introduction to PDEs and their classifications. Classic and weak solutions are covered along with numerical iterative methods to find solutions. Several common PDEs of interest are discussed; these are the Heat, Wave, Laplace, Poisson, Stokes, and Navier-Stokes equations. Methods for discretization techniques that produce large sparse matrices are presented along with the direct methods for solving; these are the LU and Cholesky factorization methods. Four iterative methods are presented in Chapter 4; these are Jacobi, Gauss-Seidel, SOR, and GMRES iteration methods. Numerical experiments were then performed via the software extension IFISS in MATLAB. Results in chapter 4 show the effectiveness and efficiency of the numerical solvers.
Details
- Title
- PARTIAL DIFFERENTIAL EQUATION MODELS AND THEIR NUMERICAL SOLUTIONS
- Resource Type
- Thesis
- Publisher
- University of West Florida
- Format
- text
- Identifiers
- 99380090728306600
- Academic Unit
- Mathematics and Statistics
- Language
- English
- Awarding Institution
- University of West Florida; Master of Science (MS)
- Theses and Dissertations
- Master of Science (MS), University of West Florida