general linear methods – Optimization Online

Construction of IMEX DIMSIMs of high order and stage order

Published: 2015/09/09, Updated: 2017/08/08

Applications - Science and Engineering construction of highly stable methods, dimsims, general linear methods, imex methods, optimization methods, stability analysis

For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stff or mildly stff, and the other part is stff. Such systems can be effciently treated by a class of implicit-explicit (IMEX) diagonally implicit multistage integration … Read more

Optimization-based search for Nordsieck methods of high order with quadratic stability

Published: 2011/01/27

A. Cardone

Z. Jackiewicz

Hans D Mittelmann

Applications - Science and Engineering general linear methods, least-squares minimization, nordsieck methods, quadratic sta- bility

We describe the search for explicit general linear methods in Nordsieck form for which the stability function has only two nonzero roots. This search is based on state-of-the-art optimization software. Examples of methods found in this way are given for order p = 5, p = 6, and p = 7. ArticleDownload View PDF