Implicit Euler and Lie splitting discretizations of nonlinear parabolic equations with delay

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

Abstract

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.

Detaljer

Författare
Enheter & grupper
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik

Nyckelord

Originalspråkengelska
Sidor (från-till)673-689
TidskriftBIT Numerical Mathematics
Volym54
Utgåva nummer3
StatusPublished - 2014
PublikationskategoriForskning
Peer review utfördJa

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Relaterad forskningsoutput

Tony Stillfjord, 2015, Centre for Mathematical Sciences, Lund University. 129 s.

Forskningsoutput: AvhandlingDoktorsavhandling (sammanläggning)

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Relaterade aktiviteter

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Aktivitet: Examination och handledarskapHandledning av forskarstuderande

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