×

zbMATH — the first resource for mathematics

Nonoscillatory high order accurate self-similar maximum principle satisfying shock capturing schemes. I. (English) Zbl 0859.65091
An approach to constructing a class of shock-capturing high-order nonoscillatory schemes for hyperbolic conservation laws is outlined using a scalar one-dimensional equation as an example. The reconstruction procedure which enforces a local maximum principle and prevents the developing of new extrema is described. It is shown that the resulting third-order scheme is nonoscillatory and possesses the total variation boundedness property. The implementation of the scheme and the numerical results are presented for the linear equation and the inviscid Burgers’ equation.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35Q53 KdV equations (Korteweg-de Vries equations)
PDF BibTeX Cite
Full Text: DOI