TVB uniformly high-order schemes for conservation laws. (English) Zbl 0628.65075

Shu, Chiwang

Math. Comput. 49, 105-121 (1987).

The author presents an analysis of total-variation-bounded (TVB) uniformly high-order schemes for conservation laws using complex mathematics. The schemes are shown to generate locally first order accuracy at nonsonic critical points. Numerical examples are provided to illustrate these schemes.

Reviewer: P.K.Mahanti

MSC:

65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65	Hyperbolic conservation laws

Keywords:

hyperbolic conservation law; total-variation-bounded uniformly high-order schemes; locally first order accuracy; nonsonic critical points; Numerical examples