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Asymptotic theory of the global error and some techniques of error estimation. (English) Zbl 0535.65075

The error of the approximate solution obtained by discretising a functional equation can be shown under certain conditions to possess an asymptotic expansion in terms of some parameter which is usually a representative step-length. We consider the case of two-parameter expansions, which is particularly relevant to parabolic equations. We derive results for the existence of the expansion and for the application of the classical difference correction and of defect correction. The theory is illustrated by the discussion of a simple parabolic problem.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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References:

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