Institute of Computational Mathematics and Mathematical Geophysics


International Conference on Mathematical Methods in Geophysics «MMG-2003»

Akademgorodok, Novosibirsk, Russia, October 8-12, 2003

Abstracts

Mathematical modeling of processes in atmosphere and hydrosphere

The Relationship Between Non-conservative Schemes of Nonlinear Evolution Equation and Initial Values

Lin W.

Institute of Atmospheric Physics/Chinese Academy of Sciences (Beijing)

For the non-conservative schemes of nonlinear evolution equations, taking one-dimensional shallow water wave equation as an example, the necessary conditions of computational stability are given. Based on the numerical tests, the relationship between the nonlinear computational stability, the construction of difference schemes, and the form of initial values is further discussed. It is proved through theoretical analysis and numerical tests that if the construction of difference schemes is definite, the computational stability of non-conservative schemes is decided to the form of initial values.

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