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Animations from Numerical and Analytical Methods for Scientists and Engineers, using Mathematica
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| Organization: | University of California, San Diego |
| Department: | Department of Physics |
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2003-03-11
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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.
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nonlinear, kdV, Galerkin, soliton, oscillating boundary, gravitational collapse
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| 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 |
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