A second-order positivity preserving scheme for semilinear parabolic problems

Summary, in English

In this paper we study the convergence behaviour and geometric properties of Strang splitting applied to semilinear evolution equations. We work in an abstract Banach space setting that allows us to analyse a certain class of parabolic equations and their spatial discretizations. For this class of problems, Strang splitting is shown to be stable and second-order convergent. Moreover, it is shown that exponential operator splitting methods and in particular the method of Strang will preserve positivity in certain situations. A numerical illustration of the convergence behaviour is included.

• Författare: Eskil Hansen; Felix Kramer; Alexander Ostermann
• Avdelning/ar: Matematik LTH; Partial differential equations; Numerical Analysis
• Publiceringsår: 2012
• Språk: Engelska
• Sidor: 1428-1435
• Publikation/Tidskrift/Serie: Applied Numerical Mathematics
• Volym: 62
• Issue: 10
• Fulltext: - 100 kB; Download statistics
• Länkar: http://dx.doi.org/10.1016/j.apnum.2012.06.003
• Dokumenttyp: Artikel i tidskrift
• Förlag: Elsevier
• Ämne: Mathematics
• Nyckelord: positivity; convergence; stability; semilinear parabolic problems; Strang splitting; invariant sets.
• Status: Published
• Forskningsgrupp: Partial differential equations; Numerical Analysis
• ISBN/ISSN/Övrigt: ISSN: 0168-9274