Институт вычислительной математики
и математической геофизики

The International Conference on Computational Mathematics


Numerical solution of differential and integral equations

On the Construction of Difference Schemes for Hyperbolic Conservation Laws with the Aid of the B"{u}rmann-Lagrange Expansions

Vorozhtsov E.V.

Institute of Theoretical and Applied Mechanics,
SB RAS (Novosibirsk)

The Lagrange-B"{u}rmann formula solves the problem of expansion of the function u(x) in powers of another function f(x). The Taylor expansion is a particular case of the B"{u}rmann-Lagrange expansion. We propose to construct the second-order difference schemes for hyperbolic conservation laws within the context of the ENO schemes of Osher et al. with the aid of the Lagrange-B"{u]rmann expansions. The requirements are discussed, which are to be satisfied by the function f(x). The numerical computations of a number of one-dimensional test problems show that it is possible to efficiently suppress the spurious oscillations of the numerical solution in the neighborhood of contact discontinuities in inviscid compressible fluid flows at the expense of a proper choice of the function f(x).

Note. Abstracts are published in author's edition

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