Analysis of Four Numerical Schemes for a Nonlinear Klein-Gordon Equation

摘要

We compare the properties of four explicit finite difference schemes used to integrate the nonlinear Klein-Gordon equation ϕtt-ϕxx+f(ϕ)=0. It turns out that the energy conserving scheme is the most suitable to study the long time behavior of the solutions. The same result is found for the special case of no spatial dependence.