Approximation of singularly perturbed reaction-diffusion problems by quadratic C 1-splines

Torsten Linß, Goran Radojev, Helena Zarin

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Collocation with quadratic C 1-splines for a singularly perturbed reaction-diffusion problem in one dimension is studied. A modified Shishkin mesh is used to resolve the layers. The resulting method is shown to be almost second order accurate in the maximum norm, uniformly in the perturbation parameter. Furthermore, a posteriori error bounds are derived for the collocation method on arbitrary meshes. These bounds are used to drive an adaptive mesh moving algorithm. Numerical results are presented.

Original languageEnglish (US)
Pages (from-to)35-55
Number of pages21
JournalNumerical Algorithms
Volume61
Issue number1
DOIs
StatePublished - Sep 2012
Externally publishedYes

Bibliographical note

Funding Information:
H. Zarin is supported by the Ministry of Education and Science of the Republic of Serbia under grant 174030.

Funding Information:
This publication has eminated from research conducted with support by the DAAD (grant no. 50740187) and the Ministry of Education and Science of the Republic of Serbia under grant “Collocation methods for singularly perturbed problems”.

Keywords

  • A posteriori error estimation
  • Reaction-diffusion problems
  • Singular perturbations
  • Spline collocation
  • Spline interpolation

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