Numerical solution of damped nonlinear Klein-Gordon equations using variational method and finite element approach

Numerical treatment for damped nonlinear Klein-Gordon equations, based on variational method and finite element approach, is studied. A semi-discrete algorithm is proposed by using quadratic interpolation functions of continuous time and spatial dimension one. The Gauss-Legendre quadrature has been utilized for numerical integrations of nonlinear terms, and Runge-Kutta method is used for solving ordinary differential equation. Finally, three dimensional graphics of numerical solutions are used to demonstrate the numerical results.