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A numerical method for first order nonlinear scalar conservation laws in one-dimension. (English) Zbl 0658.65085
A numerical method for the following initial value problem for first order nonlinear scalar hyperbolic conservation law \(u_ t+f(u)_ x=0,\) \(u(x,0)=u_ 0(x)\) is proposed. The method is to approximate f by a piecewise linear function and the initial value by a piecewise constant function. It is proved to be applicable as a numerical method for a general flux function and a general initial value. The authors also point out that the error in this method is far smaller than in any other method and illustrate the method in an example.
Reviewer: V.Kamen

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35L65 Hyperbolic conservation laws
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