Award Date

May 2023

Degree Type


Degree Name

Doctor of Philosophy (PhD)


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



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.


Meshless Methods; Method of Fundamental Solutions; Method of Particular Solutions; Numerical Boundary Value Problems; Numerical Initial Boundary Value Problems; Radial Basis Functions



Degree Grantor

University of Nevada, Las Vegas




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