On the structure of error estimates for finite-difference methods |
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Authors: | Dr M N Spijker |
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Institution: | (1) Centraal Reken-Instituut, Rijksuniversiteit Leiden, Stationsplein 20, Leiden, The Netherlands |
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Abstract: | In this paper we study in an abstract setting the structure of estimates for the global (accumulated) error in semilinear finite-difference methods. We derive error estimates, which are the most refined ones (in a sense specified precisely in this paper) that are possible for the difference methods considered. Applications and (numerical) examples are presented in the following fields: 1. Numerical solution of ordinary as well as partial differential equations with prescribed initial or boundary values. 2. Accumulation of local round-off error as well as of local discretization error. 3. The problem of fixing which methods out of a given class of finite-difference methods are most stable . 4. The construction of finite-difference methods which are convergent but not consistent with respect to a given differential equation. |
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