An enhanced Chebyshev collocation method based on the integration of Chebysehv interpolation

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Abstract

In this paper, we develop an enhanced Chebyshev collocation method based on an integration scheme of the generalized Chebyshev interpolations for solving stiffinitial value problems. Unlike the former error embedded Chebyshev collocation method (CCM), the enhanced scheme calculates the solution and its truncation error based on the interpolation of the derivative of the true solution and its integration. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have the 7th convergence order and the A-stability without any loss of advantages for CCM. Throughout a numerical result, we assess the proposed method is numerically more efficient compared to existing methods.

Original languageEnglish
Pages (from-to)287-299
Number of pages13
JournalKyungpook Mathematical Journal
Volume57
Issue number2
DOIs
StatePublished - 2017

Keywords

  • Collocation method
  • Error embedded method
  • Generalized Chebyshev polynomial
  • Integration scheme
  • Stiffinitial value problem

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