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

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Author

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.

Department/s

Publishing year

2014

Language

English

Pages

673-689

Publication/Series

BIT Numerical Mathematics

Volume

54

Issue

3

Document type

Journal article

Publisher

Springer

Topic

  • Mathematics

Keywords

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

Status

Published

Research group

  • Numerical Analysis
  • Partial differential equations

ISBN/ISSN/Other

  • ISSN: 0006-3835