Vectorized Solution of ODEs in Matlab

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L. F. Shampine

Abstract

Vectorization is very important to the efficiency of computation in the popular
problem-solving environment Matlab. It is shown that a class of Runge-Kutta
methods investigated by Milne and Rosser that compute a block
of new values at each step are well-suited to vectorization. Local error estimates and
continuous extensions that require no additional function evaluations are derived.
A (7,8) pair is derived and implemented in a program BV78 that is shown to perform quite
well when compared to the well-known Matlab ODE solver ode45 which is
based on a (4,5) pair.

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Section
Special Issue