Stability of Difference Schemes

The most powerful and most general method for constructing approximate solutions of hyperbolic partial differential equations with prescribed initial values is to discretize the space and time variables and solve the resulting finite system of equations. How to discretize is a subtle matter, as we shall demonstrate. In this report, some of the proofs are only sketched; details can be found in Chap. 8 of my monograph “Hyperbolic Partial Differential Equations”, 2006, AMS.

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