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Introduction to Hermite Methods
Ronald Chen
UNM
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Introduction to Hermite Methods Ronald Chen UNM |
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ABSTRACT We study arbitrary-order Hermite difference methods for the numerical solution of initial-boundary value problems for symmetric hyperbolic systems. These differ from standard difference methods in that derivative data (or equivalently local polynomial expansions) are carried at each grid point. Time-stepping is achieved using staggered grids and Taylor series. The methods using derivatives of order m in each coordinate direction are stable under m-independent CFL constraints and converge at order 2m+1. The stability proof relies on the fact that the Hermite interpolation process generally decreases a seminorm of the solution. We present numerical experiments demonstrating the resolution of the methods for large m as well as illustrating the basic theoretical results. |