A predictor-corrector scheme for the sine-Gordon equation

A predictor-corrector scheme is developed for the numerical solution of the sine-Gordon equation using the method of lines approach. The solution of the approximating differential system satisfies a recurrence relation, which involves the cosine function. Pade' approximants are used to replace the cosine function in the recurrence relation. The resulting schemes are analyzed for order, stability, and convergence. Numerical results demonstrate the efficiency and accuracy of the predictor-corrector scheme over some well-known existing methods. (C) 2000 John Wiley & Sons, Inc.