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Animations from Numerical and Analytical Methods for Scientists and Engineers, using Mathematica

Daniel Dubin
Organization: University of California, San Diego
Department: Department of Physics
Revision date


Once a method has been programmed in Mathematica, it is straightforward to provide instructive visualizations. Three examples are provided here:

1. A solution of the nonlinear kdV equation (using the Galerkin method) that exhibits the breakup of a smooth initial condition into solitons. 2. A solution to the linear wave equation with varying wave speed and an oscillating boundary (using the CTCS grid) 3. A gravitational collapse from a random initial condition via the particle in cell method.

More methodologies are available in the book.

*Science > Physics > Wave Motion
*Wolfram Technology > Programming > Animations

nonlinear, kdV, Galerkin, soliton, oscillating boundary, gravitational collapse
Related items

*Numerical and Analytical Methods for Scientists and Engineers Using Mathematica   [in Books]
Downloads Download Wolfram CDF Player

collapse.mov (821 KB) - 2D animation of gravitational collapse
kdV.mov (505.2 KB) - 2D animation of solitons
sec6_2_1.nb (166 KB) - Notebook for waves.mov
waves.mov (361.8 KB) - 3D animation of waves