Implicit Euler and Lie splitting discretizations of nonlinear parabolic equations with delay
Författare
Summary, in English
A convergence analysis is presented for the implicit Euler and Lie splitting schemes when applied to nonlinear parabolic equations with delay. More precisely, we consider a vector field which is the sum of an unbounded dissipative operator and a delay term, where both point delays and distributed delays fit into the framework. Such equations are frequently encountered, e.g. in population dynamics. The main theoretical result is that both schemes converge with an order (of at least) q = 1/2, without any artificial regularity assumptions. We discuss implementation details for the methods, and the convergence results are verified by numerical experiments demonstrating both the correct order, as well as the efficiency gain of Lie splitting as compared to the implicit Euler scheme.
Avdelning/ar
- Matematik LTH
- Numerical Analysis
- Partial differential equations
Publiceringsår
2014
Språk
Engelska
Sidor
673-689
Publikation/Tidskrift/Serie
BIT Numerical Mathematics
Volym
54
Issue
3
Fulltext
- Available as PDF - 212 kB
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Länkar
Dokumenttyp
Artikel i tidskrift
Förlag
Springer
Ämne
- Mathematics
Nyckelord
- Nonlinear parabolic equations
- delay differential equations
- Convergence orders
- Implicit Euler
- Lie splitting
Status
Published
Forskningsgrupp
- Numerical Analysis
- Partial differential equations
ISBN/ISSN/Övrigt
- ISSN: 0006-3835