Sinc-Galerkin Method For Two-dimensional Helmholtz Equations

This research of Sinc-Galerkin method and Sinc functions as a research base function to approximate solution of two-dimensional Helmholtz equation in physical systems will be discussed in this thesis. This research study is based on variables about space of the Helmholtz Equation, and a second-order ordinary differential equation about time. Solutions about time are linear combinations of a cosine function, space solutions must rely on boundary conditions, so long as the given boundary conditions, we can space solution. The ultimate goal of this research is the use of Sinc-Galerkin method to approximate solution of the Helmholtz Equation on Dirichlet-type boundary value.In support of this thesis the feasibility of numerical methods, the main theory of the study is to be taken: the use of numerical methods, Sinc-Galerkin method, first derive the numerical method for solving the one-dimensional boundary value; and then extended to the one-dimensional Helmholtz equation, and numerical solution of Helmholtz equation will be approximated. In the computer, program will realize numerical solution, and contrast the error of the analytical solution and numerical solution.This study also will be on the adopted numerical methods for further improvement, reduce the amount of computation and error. Once again, the one-dimensional Helmholtz equation is extended to two-dimensional Helmholtz equation. Finally, the improved method through computer program of numerical solution, is improving the numerical method of solution error with the analytical solution, further enhance the accuracy of numerical solution. The final verification shows that the Sinc-Galerkin method is a high accuracy numerical solution for two-dimensional Helmholtz equation.