The extrapolation of stable finite difference schemes for first order hyperbolic equations

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Abstract
A uniform grid of step size h is superimposed on the space variable x in the first order hyperbolic partial differential equation . The space derivative is approximated by its central difference replacement and the resulting linear system of first order ordinary differential equations is solved employing Padé approximants to the exponential function. A number of stable, two-level difference schemes for solving the hyperbolic equation are thus developed and each is extrapolated to give higher order accuracy. Some of these schemes are unconventional in that they use more than three mesh points at one or both time levels. The resulting increase in computer time is, however, negligible and the improvement in accuracy justifies their use.

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