Alternating direction implicit orthogonal spline collocation on some non-rectangular regions with inconsistent partitions

Bernard Bialecki, Ryan I. Fernandes

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The alternating direction implicit (ADI) method is a highly efficient technique for solving multi-dimensional dependent initial-boundary value problems on rectangles. Earlier we have used the ADI technique in conjunction with orthogonal spline collocation (OSC) for discretization in space to solve parabolic problems on rectangles and rectangular polygons. Recently, we extended applications of ADI OSC schemes to the solution of parabolic problems on some non-rectangular regions that allow for consistent nonuniform partitions. However, for many regions, it is impossible to construct such partitions. Therefore, in this paper, we show how to extend our approach further to solve parabolic problems on some non-rectangular regions using inconsistent uniform partitions. Numerical results are presented using piecewise Hermite cubic polynomials for spatial discretizations and our ADI OSC scheme for parabolic problems to demonstrate its performance on several regions.

Original languageBritish English
Pages (from-to)1083-1100
Number of pages18
JournalNumerical Algorithms
Volume74
Issue number4
DOIs
StatePublished - 1 Apr 2017

Keywords

  • Alternating direction implicit method
  • Crank Nicolson
  • Non-rectangular region
  • Orthogonal spline collocation
  • Parabolic equation
  • Two point boundary value problem

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