RungeKutta4

4th-order Runge-Kutta integrator, fully vectorized.

This is a simple implementation of a 4th-order, fixed-step, Runge-Kutta integrator. It is fully vectorized, which allows a large number of simulations to be carried out in parallel. It is designed to be used inside of optimization code.
% z = rk4(dyn,t,z0)
%
% This function (rk4) is used to perform a 4th-order Runge-Kutta
% integration of a dynamical system.
%
% INPUTS:
% dyn = handle of the form:
% dz = userFunc(t,z)
% t = [1 x nTime] vector of times, created by linspace
% z0 = [nState (x nSim)] matrix of initial states
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% OUTPUTS:
% z = [nState (x nSim) x nTime ] matrix of trajectories
%