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

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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.
Original languageEnglish
Pages (from-to)673-689
JournalBIT Numerical Mathematics
Volume54
Issue number3
DOIs
Publication statusPublished - 2014

Bibliographical note

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

Subject classification (UKÄ)

  • Mathematics

Keywords

  • Nonlinear parabolic equations
  • delay differential equations
  • Convergence orders
  • Implicit Euler
  • Lie splitting

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  • Tony Stillfjord

    Eskil Hansen (First/primary/lead supervisor)

    20112015

    Activity: Examination and supervisionSupervision of PhD students

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