Behind and beyond the Matlab ODE suite

Dedicated to Professor Norio Shimakura on the occasion of his 60th birthday.
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Abstract

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

describes the phenomenon of problem stiffness, and 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.

Keywords

Stiff and nonstiff differential equations
Implicit and explicit ODE solvers
Matlab odedemo

Cited by (0)

The authors thank the referee for deep and constructive remarks which improved the paper considerably. This paper is an expanded version of a lecture given by the third author at Ritsumeikan University, Kusatsu, Shiga, 525-8577 Japan, upon the kind invitation of O. Yamada whom the authors thank very warmly.