On the solution of high order stable time integration methods

0395518 - ÚGN 2014 RIV DE eng J - Journal Article
Axelsson, Owe - Blaheta, Radim - Sysala, Stanislav - Ahmad, B.
On the solution of high order stable time integration methods.
Boundary Value Problems. Roč. 108, č. 1 (2013), s. 1-22. ISSN 1687-2770. E-ISSN 1687-2770
Institutional support: RVO:68145535
Keywords : evolution equations * preconditioners for quadratic matrix polynomials * a stiffly stable time integration method
Subject RIV: BA - General Mathematics
Impact factor: 0.836, year: 2013
http://www.boundaryvalueproblems.com/content/2013/1/108

Evolution equations arise in many important practical problems. They are frequently stiff, i.e. involves fast, mostly exponentially, decreasing and/or oscillating components. To handle such problems, one must use proper forms of implicit numerical time-integration methods. In this paper, we consider two methods of high order of accuracy, one for parabolic problems and the other for hyperbolic type of problems. For parabolic problems, it is shown how the solution rapidly approaches the stationary solution. It is also shown how the arising quadratic polynomial algebraic systems can be solved efficiently by iteration and use of a proper preconditioner.
Permanent Link: http://hdl.handle.net/11104/0231695