Numerical solution of Cauchy problem for second order nonlinear wave equation with changeable type in a class of discontinues functions

Abstract

In this paper, a special numerical method for the solution of second order nonlinear wave equation with changeable type in a class of discontinues functions, which accurately describe the physical properties of the problem of interest is suggested. For this, first, an auxiliary problem having some advantages over the main problem is introduced. Since, the differentiable property of the solution of the auxiliary problem is twice higher than the differentiability of the solution of the main problem, the application of classical methods to the auxiliary problem can be easily performed. Some economic algorithms are proposed for obtaining a numerical solution of the auxiliary problem, and by using the solution of the auxiliary problem, the numerical solution of the main problem is also found. In order to show the effectiveness of the suggested algorithms some comparisons between the exact solution and the numerical solution are made.