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AVERAGING OF DIFFERENCE SCHEMES
Mathematics of the USSR-Sbornik, 1987The author considers the family of difference operators \(A_{\epsilon}u=\epsilon^{-2}(\sum_{y}p^{\epsilon}(x,y)u(y)-u(x))\) on the uniform grid of the mesh \(\epsilon\) ; x,y\(\in Q\), a bounded domain in \(R^ n\). Here \(p^{\epsilon}(x,y)=p^{\epsilon}(y,x)\geq 0\) (x\(\neq y)\); \(| p^{\epsilon}(x,x)| c,\epsilon\); \(\sum_{i}p^{\epsilon}(x,x+\epsilon ...
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Journal of Computational Physics, 1999The article is the keynote address given by the author at the symposium ``Gudunov's method for gas dynamics: Current applications and future developments'' held at Michigan University in May 1997 in honour of S. K. Godunov. It is concerned with which is nowadays called ``Godunov's scheme'' and its later modifications.
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