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http://dx.doi.org/10.5666/KMJ.2011.51.4.435

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)
Publication Information
Kyungpook Mathematical Journal / v.51, no.4, 2011 , pp. 435-456 More about this Journal
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.
Keywords
Chebyshev Collocation method; BDF-type methods; Stiff initialvalue problem; Absolute stability;
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