Applied Math Seminar
Quarter 2001
3:15 - 4:15 p.m.
Sloan Mathematics Corner
Building 380, Room 380-C

November 30, 2001


Zhiqiang Cai
Purdue University

Rate of Corrections and its Application in Scientific Computing

Abstract:

One of the major issues in numerical analysis/scientific computing is the accuracy of the underlying numerical methods. It is a common knowledge that the accuracy of all current numerical methods for differentiation, integration, ordinary and partial differential equations etc are limited by the highest derivative of the underlying approximated function. This talk presents an approach for computing higher order accurate approximations when the approximated functions are not smooth. The key idea of this work is the introduction of a rate of corrections that is of universality, that quantifies the accuracy of the numerical method used, and that is computationally feasible. The rate of corrections is then used to increase the accuracy of the approximation. Also, this approach can be applied to problems without continuum background, such as the sequence of period-doubling bifurcations in chaos.

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