Mathematica Articles


Robert Knapp and Stan Wagon, "Check Your Answers... But How?", Mathematica in Education and Research, Vol. 7 No. 4, Fall 1998.

This articles shows some techniques for ensuring that the result you get from NDSolve is sufficiently accurate. These techniques are useful because even though NDSolve has a good local error control mechanism, sometimes global error gets out of hand.

Robert Knapp and Mark Sofroniou, "Some Numerical Aspects of Functional Iteration and Chaos in Mathematica", Dr. Dobbs Journal, October 1997.

Downloadable from MathSource as a Mathematica notebook .


Robert Knapp, "Partial Differential Equations", Mathematica Journal, Vol. 6, No. 4, Fall, 1996.

This article describes the partial differential equation solving capability of the Mathematica NDSolve function which is new to version 3.0. Several examples are given which show how to use various options of the method.

Robert Knapp and Stan Wagon, "Orbits you can bet on", CODEE newsletter.

Downloadable from MathSource as a Mathematica notebook .

This article examines how one can compute accurate orbits to systems of ODE's which are sensitive to initial conditions. The Duffing equation is used as an example to show how inaccurate orbits can be detected, their cause (discussed in terms of the Lyapunov characteristic exponent), and a method that can be used to compute accurate orbits.


Robert Knapp rknapp@wri.com

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