Vectorized Solution of ODEs in Matlab

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.