A coupling technique based on method of line and group preserving scheme for solving the nonlinear wave equation - Partohaghighi, Mohammad; Hesameddini, Esmail; İnç, Mustafa (Taylor & Francis Ltd, 2021)
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.
Keywords: Group preserving scheme; Nonlinear wave equation; Line method