lajos/2013spring

Interesting conferences

June 2-5: Workshop, KAUST
June 11-12: European Technology Conference (Wolfram), Frankfurt ?
July 1-5: Erdős Centennial, Budapest ?
July 15-19: International Conference on Delay Differential and Difference Equations and Applications, Balatonfüred, Hungary ?

Joint paper with David, Matteo and Yiannis. Add the internal stability estimates for optimal \(3^{\mathrm{rd}}\) order explicit SSP Runge-Kutta methods. Add the internal stability estimates for the extrapolation methods (closed-form solution of the partial difference equation, some results on the gamma function the \(W\)-function, lower and asymptotic bounds on the maximum).

Can the global attractivity result (on the two-term non-linear recursion) be embedded in a more general setting?
In connection with the internal stability of extrapolation methods, can we prove the semi-disk property rigorously from the integrals \(I_1\), \(I_2\) and \(J\)? With the reference provided by Tihi, the answer is yes.
Linear programming in Mathematica with higher precision?
Investigate David’s observations on the monotonicity properties and on the patterns in connection with the numbers \(R_{s, p, k}\), i.e., the optimal threshold factors for explicit general linear methods with \(s\) stages, \(k\) steps, and order at least \(p\).
With David and Matteo we have some results on the maximal disks/ellipses contained in the spectrum, in connection with predicting upper bounds on the effective time steps.
Following Igor’s work (based on a paper of Hundsdorfer-Mozartova-Spijker), what can we say about the non-negativity of the sequences arising in connection with multistep methods and generated by linear recursions?