Doctor of Philosophy (PhD)
First Committee Member
Second Committee Member
Third Committee Member
Fourth Committee Member
Number of Pages
In this dissertation we propose and examine numerical methods for solving the boundary value problems of partial differential equations (PDEs) by meshless methods. First we aim at getting approximate particular solutions up of a nonhomogeneous equation by radial basis methods. For instance, the collocation method by radial basis functions (RBFs) for finding particular solutions is very popular in the literature. Now the particular solutions of certain important PDEs by RBF approximation are available with the order of convergence to the exact solutions provided. Here we explore and examine the numerical performances of these particular solutions in various examples. We then consider and solve the following boundary value problems of the homogeneous equation by the methods of fundamental solutions (MFS). Choose a fictitious domain and choose some collocation points on boundary of domain and some source points on boundary of fictitious domain Then we have an approximate solution vn of the homogeneous equations by MFS. Hence, u(x) = up(x) + vn(x) is considered as the numerical solution of our original problem. In this dissertation, we present various examples to show the efficiencies of the above mentioned methods, especially for Poisson’s, Helmholtz, and biharmonic equations of Dirichlet, or Newmann, or Robin (Mixed) boundary conditions, with numerical results provided correspondingly in tables and graphs.
University of Nevada, Las Vegas
Choi, Minhwa, "Meshless Methods for Numerically Solving Boundary Value Problems of Elliptic Type Partial Differential Equations" (2018). UNLV Theses, Dissertations, Professional Papers, and Capstones. 3232.
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