A coupling technique based on method of line and group preserving scheme for solving the nonlinear wave equation

Abstract

In this work, a powerful approach is presented to solve the nonlinear wave equation (NWE): u(tt) (x, t) - u(x, t)u(xx) (x, t) = g(x, t), where c is a positive constant. Firstly, a discretization is implemented on the original equation. Then, a geometric technique is applied to obtain the approximate solutions. Some examples are displayed to prove the power and capability of the offered approach to work out the wave problem.