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

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Sammanfattning

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.
Originalspråkengelska
Sidor (från-till)673-689
TidskriftBIT Numerical Mathematics
Volym54
Utgåva3
DOI
StatusPublished - 2014

Bibliografisk information

The information about affiliations in this record was updated in December 2015.
The record was previously connected to the following departments: Numerical Analysis (011015004)

Ämnesklassifikation (UKÄ)

  • Matematik

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  • Tony Stillfjord

    Eskil Hansen (Första/primär/huvudhandledare)

    20112015

    Aktivitet: Examination och handledarskapHandledning av forskarstuderande

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