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Uniformly high order accurate essentially non-oscillatory schemes. III. (English) Zbl 0652.65067
[For part I cf. the first and the third author, SIAM J. Numer. Anal. 24, 279-309 (1987; Zbl 0627.65102).]
The authors continue the studying of essentially nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws. New schemes which generalize Godunov’s scheme and its second-order extension are constructed. Algorithms for numerical solution of the Euler equations of gas dynamics are described and some numerical experiments are discussed.
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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