On the Numerical Solution of the Sine-Gordon Equation in 2+1 Dimensions

摘要

The method of lines is used to transform the initial/boundary-value problem associated with the Sine-Gordon equation in two space variables, into a first-order, initial-value problem. The finite-difference methods are developed by replacing the matrix-exponential term in a recurrence relation by rational approximants. The resulting finite-difference methods are analyzed for local truncation error, stability and convergence. Numerical solutions for cases involving the most known from the bibliography ring and line solitons are given.