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A new method of constructing a completely conservative difference scheme for hyperbolic differential equations in three dimensions. (Chinese. English summary) Zbl 1010.35069

Summary: A completely conservative difference scheme for hyperbolic differential equations in three dimensions is studied. A parameter algorithm is introduced for three-dimensional Euler hydrodynamic equations. It is shown that the parameters have to satisfy some conditions if the completely conservative difference schemes are to be constructed. It is proved that these schemes have second-order accuracy. And the schemes with undetermined parameters are constructed for the three-dimensional Euler equations of nonviscous, nonconducting, compressible fluid flow.

MSC:

35L60 First-order nonlinear hyperbolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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