Award Date
May 2023
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
First Committee Member
Xin Li
Second Committee Member
Douglas Burke
Third Committee Member
Rohan Dalpatadu
Fourth Committee Member
Jeehee Lee
Number of Pages
113
Abstract
In this dissertation, the methods of fundamental solutions (MFS) and the methods of particular solutions (MPS) are used to solve the boundary value problems of the Poisson and Helmholtz equations, where the particular solutions of the Poisson and Helmholtz equations in [13, 14] are used. Then the initial boundary value problems of the diffusion and wave equations are discretized into a sequence of boundary value problems of the Helmholtz equation by using either the Laplace transform or time difference methods along the lines of [8]. The Helmholtz problems are solved consequently in an iterative manner which leads to the solution of the original diffusion or wave equation. Various numerical examples are presented in this dissertation to show the efficiencies of the purposed methods. Some further work including solving Stoke's flow problems is also purposed here.
Keywords
Meshless Methods; Method of Fundamental Solutions; Method of Particular Solutions; Numerical Boundary Value Problems; Numerical Initial Boundary Value Problems; Radial Basis Functions
Disciplines
Mathematics
File Format
Degree Grantor
University of Nevada, Las Vegas
Language
English
Repository Citation
Johnson, Adam, "Solving Boundary Value and Initial Boundary Value Problems of Partial Differential Equations Using Meshless Methods" (2023). UNLV Theses, Dissertations, Professional Papers, and Capstones. 4716.
http://dx.doi.org/10.34917/36114741
Rights
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