Abstract
The method of lines is used to transform the initial/boundary-value problem assckiated with the nonlinear hyperbolic sine-Gordon equation, into a first-order, nonlinear, initial-vjalue problem. Numerical methods are developed by replacing the matrix-exponential term \n a recurrence relation by rational approximants. The resulting finite-difference methods ar|e analysed for local truncation errors, stability and convergence. The results of a number of numerical experiments are given.
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