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Report 1996-17
Asymptotically Optimal Approximation and Numerical Solutions of Differential Equations
M.D. Buhmann, Ch.A. Micchelli and A. Ron
Abstract: An optimal finite difference method for the numerical solution of the Cauchy problem for a given partial differential equation is, by definition, the scheme that minimises the local truncation error after one step. In this paper we conduct a study of certain extremal problems that are closely related to optimal finite difference schemes for finding numerical solutions of such problems.
Paper: Available as PDF (337 KB) or as hardcopy to order reports@sam.math.ethz.ch.
Publishing information: Approximation Theory and Optimization. Tributes to M.J.D. Powell. Editors: M.D. Buhmann and A. Iserles. Cambridge University Press, (1997)
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