GEOMETRIC INTEGRATION BY SOLUTION INTERPOLATION

Pilwon Kim ()
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Pilwon Kim: Department of Mathematics, Ohio State University, Ohio, USA

International Journal of Modern Physics C (IJMPC), 2009, vol. 20, issue 02, 313-322

Abstract: Numerical schemes that are implemented by interpolation of exact solutions to a differential equation naturally preserve geometric properties of the differential equation. The solution interpolation method can be used for development of a new class of geometric integrators, which generally show better performances than standard method both quantitatively and qualitatively. Several examples including a linear convection equation and a nonlinear heat equation are included.

Keywords: Geometric integration; numerical method; exact solutions; polynomial interpolation (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1142/S0129183109013637

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