Doctor of Philosophy (PhD)
First Committee Member
Second Committee Member
Third Committee Member
Fourth Committee Member
Number of Pages
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 . 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.
Meshless Methods; Method of Fundamental Solutions; Method of Particular Solutions; Numerical Boundary Value Problems; Numerical Initial Boundary Value Problems; Radial Basis Functions
University of Nevada, Las Vegas
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.
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