Hermite collocation solution of near-singular problems using numerical coordinate transformations based on adaptivity

A. Lang, D.M. Sloan

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A coordinate transformation approach is described that enables Hermite collocation methods to be applied efficiently in one space dimension to steady and unsteady differential problems with steep solutions. The work is an extension of earlier work by Mulholland et al. (J. Comput. Phys. 131 (1997) 280). A coarse grid is generated by an adaptive finite difference method and this grid is used to construct a steady or unsteady coordinate transformation that is based on monotonic cubic spline approximation. An uneven grid is generated by means of the coordinate transformation and the differential problem is solved on this grid using Hermite collocation. Numerical results are presented for steady and unsteady problems.
Original languageEnglish
Pages (from-to)499-520
Number of pages21
JournalJournal of Computational and Applied Mathematics
Volume140
Issue number1-2
DOIs
Publication statusPublished - 2002

Keywords

  • Adaptivity
  • Equidistribution
  • Moving meshes
  • Hermite collocation

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