Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A Chebyshev Collocation Method for Stiff Initial Value Problems and Its Stability

  • Kim, Sang-Dong (Department of Mathematics, Kyungpook National University) ;
  • Kwon, Jong-Kyum (Department of Mathematics, Kyungpook National University) ;
  • Piao, Xiangfan (Department of Mathematics, Kyungpook National University) ;
  • Kim, Phil-Su (Department of Mathematics, Kyungpook National University)
  • Received : 2011.08.03
  • Accepted : 2011.09.27
  • Published : 2011.11.23
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Abstract

The Chebyshev collocation method in [21] to solve stiff initial-value problems is generalized by using arbitrary degrees of interpolation polynomials and arbitrary collocation points. The convergence of this generalized Chebyshev collocation method is shown to be independent of the chosen collocation points. It is observed how the stability region does depend on collocation points. In particular, A-stability is shown by taking the mid points of nodes as collocation points.

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References

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