Numerical solution of two-dimensional wave equation using crank-nicolson scheme

Abstract

In this thesis, Crank-Nicholson method is presented for solving two-dimensional wave equation. First the given two-dimensional wave equation is replaced by crank-Nicholson scheme. The resulting large number of algebraic equation was arranged in order to get a block matrix. From block matrix we obtain system of linear algebraic equation and changes to tridiagonal matrices by collecting like terms. Thus the tridiagonal system of equation can solve by Thomas Algorithm. The stability, consistency and convergence of the method have been established. We implement the numerical scheme by computer programming for initial boundary value problem and compare the exact solution with the numerical solution. The results have been presented in Tables 1 to 2 for different values of some mesh points. Then, Crank-Nicolson method is good for solving two-dimensional homogeneous wave equation, since it is easy to solve the resulting tridiagonal system of equations.