An Explicit Finite Difference Scheme for Sine-Gordon Equation in Two Dimensions

Abstract

In this paper, we aim to construct an explicit finite difference scheme for solving the two-dimensional sine\u2013Gordon equation. By using Taylor expansion, we prove that the local truncation error of the scheme is of $o(h^2+\tau^2)$ with grid size $h$ and time step $\tau.$ Numerical results are reported to test the theoretical analysis.