Award Date

1-1-2005

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

C. S. Chen

Number of Pages

85

Abstract

In recent years, the method of fundamental solutions (MFS) has emerged as a novel meshless method in the scientific computing community. In the past, the MFS was essentially restricted to solving homogeneous elliptic equations. Recently, the MFS has gradually extended to solving various types of elliptic and time-dependent problems through the uses of radial basis functions (RBFs); In this thesis, we focus on solving wave equations through the MFS. Currently, there are two major approaches to solve the wave equation: (i) elimination of the time dependence by using the Laplace transform and (ii) discretization in time to approximate the time derivative. We propose to reduce the given wave equations to a series of inhomogeneous modified Helmholtz equations. The solution can then be split into evaluating both homogeneous and particular solutions. To evaluate the homogeneous solution, the MFS is adopted. Furthermore, a closed form particular solution is required for the proposed method. Intensive numerical tests are performed to compare the advantages and disadvantages of these two approaches.

Keywords

Equations; Fundamental; Method; Solutions; Solving; Wave

Controlled Subject

Mathematics; Computer science

File Format

pdf

File Size

2191.36 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

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