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Une famille de schémas numériques T.V.D. pour les lois de conservation hyperboliques. (A family of total variation diminishing numerical schemes for hyperbolic conservation laws). (French) Zbl 0623.65093
The author considers the numerical solution of the Cauchy problem for hyperbolic conservation laws. The family of numerical schemes of total variation diminishing type are constructed. Godunov’s and Glimm’s schemes are included. Particular properties of the numerical approximations are investigated. In the scalar case stability and convergence to the weak entropy solution of the problem are proved. Some numerical results are presented.
Reviewer: S.Gocheva-Ilieva
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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