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On dispersive difference schemes. I. (English) Zbl 0647.65062

Let be given a partial differential equation with a small parameter p, and consider a semi-discrete approximation with the discretization span h. The purpose of this study is to show that, under some given conditions, the approximate solution behaves in its dependence on h as the exact solution do in its dependence on p. As usual, the study of the difference equation is trickier than that of the differential equation; and one considers its smooth solutions as well as its oscillatory solutions. The effect of the breakdown time on the convergence of the approximate solution is analyzed, and mainly, beyong this instant, the oscillatory approximate solution converges to a nonsolution of the initial equation.
Reviewer: G.Jumarie

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations
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