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Scale diversity problem in numerical solution of evolutionary systems. (Russian. English summary) Zbl 0880.65062

The author analyzes the main sources of difficulties encountered by traditional numerical methods in circumstances when the scale diversity of the terms involved is large. Some additional requirements are imposed that should be taken into account while constructing new effective numerical methods for ordinary differential equations. The paper is based on a lecture given by the author for secondary school teachers in the framework of the “International Soros Science Educational Program” and is aimed at presenting contemporary developments in mathematics on an elementary level understandable for secondary school teachers and pupils.
The definition of simple waves is not that for the classical shallow-water equations.

MSC:

65L12 Finite difference and finite volume methods for ordinary differential equations
00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)
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