Monday, March 25, 2013

C^1-Lohner IVP solver specification

Last week Jan started looking at Zgliczyński's paper C^1-Lohner algorithm as a source for the specification of an IVP solver that can produce narrowing enclosures for systems with asymptotically stable solutions. The paper proved to be written in a very accessible style, and after resolving the usual notational ambiguity Jan found the presentation to clearly specify an algorithm up to choices of concrete algorithms for computing components, such as a Taylor method, or a QR decomposition. As always, when provided with a functional specification as this one, the computational mathematician will still be left to make the appropriate choices of data structures and concrete instances of algorithms. These are the tasks that Jan will target next.