A Dufort-Frankel Difference Scheme for Two-Dimensional Sine-Gordon Equation

摘要

A standard Crank-Nicolson finite-difference scheme and a Dufort-Frankel finite-difference scheme are introduced to solve two-dimensional damped and undamped sine-Gordon equations. The stability and convergence of the numerical methods are considered. To avoid solving the nonlinear system, the predictor-corrector techniques are applied in the numerical methods. Numerical examples are given to show that the numerical results are consistent with the theoretical results.