A family of parametric finite-difference methods for the solution of the sine-Gordon equation

摘要

A family of finite difference methods is used to transform the initial/boundary-value problem associated with the nonlinear hyperbolic sine-Gordon equation, into a linear algebraic system. Numerical methods are developed by replacing the time and space derivatives by finite-difference approximants. The resulting finite-difference methods are analysed for local truncation errors, stability and convergence. The results of a number of numerical experiments are given.