Titlebook: Computer Algebra Recipes; A Gourmet’s Guide to Richard H. Enns,George C. McGuire Textbook 2001 Springer Science+Business Media New York 200

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Linear ODE Models Typically, college science students do not begin to deal seriously with linear ODEs until their second and third years, starting out with equations which have constant coefficients and then moving on to special ODEs with variable coefficients such as Bessel’s equation, the Legendre and Hermite equa

ORBIT

Nonlinear ODE Modelse attempting to solve the model equations. An example was the period doubling route to chaos exhibited by the Duffing equation . when the amphtude . of the driving force was increased, the other parameters being held fixed. If the nonlinear term, β.., were not present, this “bizarre” period doubling

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Fractal Patternsa zebra we probably first think of its most prominent feature, its stripes. When we look at certain butterflies, it is usually the colorful markings on the wings that grab our attention. If we study magnified ice crystals, our interest is captivated by the richness and regularity of the patterns dis

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Diagnostic Tools for Nonlinear Dynamicsase-plane portraits and the location and identification of the relevant stationary points of the ODE system. For nonlinear maps, discussed in Chapter 8, similar graphical constructions also proved useful for understanding the behavior of the map as a control parameter was changed.

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Nonlinear PDE Models: Soliton Solutionsumerical schemes to linear and nonlinear PDEs will be given in Chapter 14. There exist special analytic solutions to some nonhnear PDEs of physical interest, the most well-known being so-called . solutions of nonlinear wave equations, the subject of this chapter. A soliton is a stable . or pulse. A