On the nonlinearity of modern shock-capturing schemes. (English) Zbl 0653.65066

Harten, Ami

Wave motion: theory, modelling, and computation, Proc. Conf. Hon. 60th Birthday P.D. Lax, Publ. Math. Sci. Res. Inst. 7, 147-201 (1987).

[For the entire collection see Zbl 0638.00016.]
This paper gives a survey of total-variation-diminishing schemes and essentially nonoscillatory schemes for nonlinear systems of hyperbolic equations. The paper is an excellent introduction to the subject.

Reviewer: G.Hedstrom

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
76N15	Gas dynamics, general
35L60	First-order nonlinear hyperbolic equations

Keywords:

shock-capturing schemes; nonlinear hyperbolic systems; total-variation- diminishing schemes; essentially nonoscillatory schemes