Behind and beyond the MATLAB ODE suite

The paper explains the concepts of order and absolute stability of numerical methods for solving systems of first-order ordinary differential equations (ODE) of the form y' = f(t, y), y(t(0)) = y(0), where f: R x R-n --> R-n, describes the phenomenon of problem stiffness, sind reviews explicit Runge-Kutta methods, and explicit and implicit linear multistep methods. It surveys the five numerical methods contained in the MATLAB ODE suite (three for nonstiff problems and two for stiff problems) to solve the above system, lists the available options, and uses the odedemo command to demonstrate the methods. One stiff ode code in MATLAB can solve more general equations of the form M(t)y' = f(t, y) provided the Mass option is on. (C) 2000 Elsevier Science Ltd. All rights reserved.