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Department of Mathematics

On the Importance (and Perils) of Being Skew-Symmetric

Prof. Arieh Iserles

Department of Applied Mathematics and Theoretical Physics
University of Cambridge
Cambridge, UK


Date: 17 March 2014 (Monday)

3:30pm - 4:30pm (Preceded by Reception at 3:00pm)

Venue: RRS905, Sir Run Run Shaw Building,
Ho Sin Hang Campus, Hong Kong Baptist University


In this talk we go back to the very basics of numerical analysis of PDEs, stability theory of finite difference schemes for linear evolution equations with variable coefficients. We prove that a universal "magic wand" renders numerical methods stable: the (first) space derivative should be discretised by a skew-symmetric matrix. The downside, however, is a barrier of 2 on the order of such methods on uniform grids. We derive a general theory coupling grid structure with the availability of skew-symmetric matrices corresponding to high-order methods.




All are welcome