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The geometric integration of scale-invariant ordinary and partial differential equations. (English) Zbl 0974.65095

A synthesis of adaptive mesh methods with the use of symmetry to solve ordinary and partial differential equations is examined. The effectiveness of numerical methods in preserving geometric structures of the underlying equations, such as scaling invariance, conservation laws, and solution orderings, is studied. The examples include the porous medium equation and the nonlinear Schrödinger equation.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
76S05 Flows in porous media; filtration; seepage

Software:

diffgrob2; DASSL
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Full Text: DOI

References:

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