On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe. (English) Zbl 0547.65065

On the basis of the inviscid Burgers equation the differencing schemes, presented here, are compared. It follows from the comparison that when conservative differencing schemes are described there are no reasons for one to reject the Godunov scheme. Nevertheless, the scheme of Roe with its modification is simpler than the Godunov scheme. The Godunov scheme, applied to nonlinear hyperbolic Euler schemes, economizes the computing memory, and the scheme of Engquist-Osher the time for computation, since it is not needed for making iterations on every time level. The conclusions about the modified Roe scheme are rather beforehand because of lacking a sufficient quantity of numerical experiments.
Reviewer: I.N.Molčanov


65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35Q99 Partial differential equations of mathematical physics and other areas of application


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