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A critical analysis of the modified equation technique of warming and Hyett. (English) Zbl 0689.65059
The cited technique by R. F. Warming and B. J. Hyett [ibid. 14, 159-179 (1974; Zbl 0291.65023)] (which helps to analyze difference methods for hyperbolic and parabolic differential equations) is investigated critically. Considering it step by step, giving counterexamples etc., the concept of the modified equation is shown to be mathematically not well-defined (the equation being of infinite order, its boundary conditions not fixed.
What remains usuable from the technique is the procedure to determine the coefficients of a series development of the logarithm of the amplification factor (in case of schemes with more than two time-levels: the principal root).
Reviewer: G.Stoyan

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
Full Text: DOI
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