Discrete and Continuous Dynamical Systems-Series B
This work explores the use of numerical experiments in two specific cases: (1) the discovery of two families of exact solutions to the elastic string equations, and approximately periodic solutions that appear to exist near pseudo-solutions formed from these families; (2) the study of the diffusion-reaction-conduction process in an electrolyte wedge (meniscus corner) of a current-producing porous electrode. This latter work establishes the well-posedness of the electrolyte wedge problem and provides asymptotic expansions for the current density and total current produced by such a wedge. The theme of this paper is the use of computing to discover a result that is difficult or impossible to find without a computer, but which once observed, can then be proven mathematically.
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© 2003, AIMS.
Fehribach, J. D. (2003). Using Numerical Experiments to Discover Theorems in Differential Equations. Discrete and Continuous Dynamical Systems-Series B, 3(4), 495-504. Retrieved from https://digitalcommons.wpi.edu/mathematicalsciences-pubs/64