An embedded formula of the Chebyshev collocation method for stiff problems

Xiangfan Piao, Sunyoung Bu, Dojin Kim, Philsu Kim

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

In this study, we have developed an embedded formula of the Chebyshev collocation method for stiff problems, based on the zeros of the generalized Chebyshev polynomials. A new strategy for the embedded formula, using a pair of methods to estimate the local truncation error, as performed in traditional embedded Runge–Kutta schemes, is proposed. The method is performed in such a way that not only the stability region of the embedded formula can be widened, but by allowing the usage of larger time step sizes, the total computational costs can also be reduced. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have an 8th order convergence and it exhibits A-stability. Through several numerical experimental results, we have demonstrated that the proposed method is numerically more efficient, compared to several existing implicit methods.

Original languageEnglish
Pages (from-to)376-391
Number of pages16
JournalJournal of Computational Physics
Volume351
DOIs
StatePublished - 15 Dec 2017

Keywords

  • Collocation method
  • Embedded formula
  • Generalized Chebyshev polynomial
  • Stiff initial value problem

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