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On the derivation of the modified equation for the analysis of linear numerical methods. (Sur le calcul des équations équivalentes pour l’analyse des méthodes numériques linéaires.) (French) Zbl 0806.65089
Summary: The modified equation is a powerful tool for the error analysis of the numerical solution of partial differential equations. We present here several remarks which considerably simplify the derivation of this equation in the linear case.

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
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