By Cleve Moler, MathWorks
After matrices, ordinary differential equations—ODEs—are the most important mathematical objects in MATLAB®. ODEs are also at the heart of Simulink® modeling and simulation capabilities. For many years, MATLAB has had only two ODE solvers available, ode23 and ode45. Even though they employ fairly simple algorithms, they have proved remarkably effective. Simulink provides some additional methods, but they are not easily accessible to MATLAB users. We have recently developed a suite of new, more powerful, ODE solvers for MATLAB.
In this article, originally published in 1996, Cleve Moler describes the applications and capabilities of the five ODE solvers available in MATLAB 5 and Simulink 2.