University of Cambridge Numerical Analysis Reports High Order Numerical Integrators for Diierential Equations Using Composition and Processing of Low Order Methods High Order Numerical Integrators for Diierential Equations Using Composition and Processing of Low Order Methods
نویسنده
چکیده
In this paper we show how to build high order integrators for solving ordinary diierential equations by composition of low order methods and using the processing technique. From a basic p-th order method, p , one can obtain high order integrators in the processed form n = P K P ?1 (n > p) being both the processor P and the kernel K compositions of the basic method. The number of conditions for the kernel is drastically reduced if we compare with a standard composition. The particular case in which p is a symmetric scheme of order 2 and 4, respectively, is analysed, and new optimised 6-th and 8-th order integrators are built.
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