Fatemeh Mohammadi (Lund University), Carmen Arévalo, Claus Führer
It is common to use BDF methods to solve index 2 DAE systems numerically even for non-stiff state space form of a problem. Because the solution with non-stiff integrators such as Adams-Moulton discretizations, is unstable. A technique designed to overcome this instability is \(\beta\)-blocking [1,2,4]. This stabilizing technique was developed for fixed step-size multistep methods.
In this talk we present a polynomial formulation of \(\beta-\)blocked multistep methods [3] that allows the use of variable step-sizes by construction. We formulate adaptive singular and regular \(\beta-\)blocked multistep methods and demonstrate their performance by some numerical examples.
References
[1] Hairer, Ernst and Wanner, Gerhard. Solving ordinary differential equations II, stiff and differential-algebraic equations. In Springer Series in Computational Mathematics, Volume 14. Springer Berlin, 1996.
[2] Arévalo, Carmen and Führer, Claus and Söderlind, Gustaf. Regular and singular \(\beta\)-blocking of difference corrected multistep methods for nonstiff index-2 DAEs. Applied numerical mathematics 35(4): 293–305, 2000.
[3] Arévalo, Carmen and Söderlind, Gustaf. Grid-independent construction of multistep methods. Journal of Computational Mathematics 35(5):670-690, 2017.
[4] Arévalo, Carmen and Führer, Claus and Söderlind, Gustaf. \(\beta\)-blocked Multistep Methods for Euler-Lagrange DAEs: Linear Analysis. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 77(8): 609–617, 1997.