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New visualization ideas for differential equations. (English) Zbl 0913.65067

Borwein, J. (ed.) et al., Organic mathematics. Proceedings of the workshop, Simon Fraser University, Burnaby, Canada, December 12-14, 1995. Providence, RI: American Mathematical Society. CMS Conf. Proc. 20, 357-381 (1997).
D. Schwalbe (Macalester College) and I have produced a comprehensive Mathematica package for the visualization of differential equations [VisualDSolve: visualizing differential equations with Mathematica (1997; Zbl 0869.34002)]. While most of the functions in it present solutions to differential equations in familiar graphical forms, we have introduced several ideas that go beyond what has been commonly done.
In this article, I will discuss one such feature, the use of shaded nullcline plots to gain insight into the phase plane. Section 1 contains a discussion of an important preliminary function that is very useful in its own right: Equilibria finds all the equilibrium points in a given rectangle. Then Section 2 presents the algorithm that produces shaded nullcline plots.
For the entire collection see [Zbl 0872.00022].

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65Y15 Packaged methods for numerical algorithms
34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
68W30 Symbolic computation and algebraic computation
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)

Citations:

Zbl 0869.34002
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