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

摘要

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.