APPROXIMATE SOLUTION BY FINITE DIFFERENCE OF A WAVE EQUATION WITH FOURTH-ORDER DERIVATIVE TERM

Abstract

This paper examines a nonlinear wave equation with a fourth-order derivative term. First, we state the results of the existence and uniqueness of the problem, which are proved by the Faedo-Galerkin method and several arguments of compactness. Next, we consider a special case of the original problem and utilize the finite difference method to construct an algorithm to find an approximate solution to the problem. In addition, we also establish some tables to estimate the error of the approximate solution and the exact one respectively iterative steps and sizes of differential mesh. Finally, we show some figures to illustrate the approximate solution and the exact solution with several various meshes.