DIFFERENCE SCHEME METHOD FOR THE NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS

In this study, wave equations with initial boundary conditions have been studied. The general form of the wave equation has been derived. The first order and second order difference schemes were established for the presented IBVP. The stability of the difference schemes has been guaranteed. The approximation solution of the problem was achieved by using finite difference methods. Two different examples are provided. A comparison between the exact and approximation solution has been carried out. Absolute errors of the problem have been presented by using MATLAB software. Moreover, the comparison shows that the second order difference scheme is a more accurate result than the first order. It is shown that the results of the comparison guaranty the reliability and accuracy of the presented method.