Multiquadric collocation method with integralformulation for boundary layer problems

Leevan LING*, M. R. Trummer

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

24 Citations (Scopus)


Singularly perturbed boundary value problems often have solutions with very thinlayers in which the solution changes rapidly. This paper concentrates on the case where theses layers occur near the boundary, although our method can be applied to problems with interior layers. One technique to deal with the increased resolution requirements in these layers is the use of domain transformations. A coordinate stretching based transform allows to move collocation points into the layer, a requirement to resolve the layer accurately. Previously, such transformations have been studied in the context of finite-difference and spectral collocation methods. In this paper, we use radial basis functions (RBFs) to solve the boundary value problem. Specifically, we present a collocation method based on multiquadric (MQ) functions with an integral formulation combined with a coordinate transformation. We find that our scheme is ultimately more accurate than a recently proposed adaptive MQ scheme. The RBF scheme is also amenable to adaptivity.

Original languageEnglish
Pages (from-to)927-941
Number of pages15
JournalComputers and Mathematics with Applications
Issue number5-6
Publication statusPublished - Sept 2004

Scopus Subject Areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

User-Defined Keywords

  • Boundary layer
  • Boundary layer problems
  • High-order discretizations
  • Integral formulation
  • Multiquadric
  • Spectral accuracy


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