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Uniformly high-order accurate nonoscillatory schemes. I. (English) Zbl 0627.65102
A new class of second order approximations of nonoscillatory schemes is constructed, in which the solution operator is only required to diminish the number of local extrema in the numerical solution. This properties are achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages.
Reviewer: P.I.Ialamov

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
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