Stability of Chebyshev collocation methods

  • Costabile F
  • Napoli A
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Abstract

In [1], a class of global collocation methods for the numerical solution of systems of nonlinear first-order ordinary differential equations was derived. The favorable comparison with other existing methods stimulated us to study them in depth. So in this paper the equivalent implicit Runge-Kutta methods are derived and their stability is studied. Methods derived in [1] are A-stable at least at up to order 20. © 2004 Elsevier Ltd.

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Costabile, F., & Napoli, A. (2004). Stability of Chebyshev collocation methods. Computers & Mathematics with Applications, 47(4–5), 659–666. https://doi.org/10.1016/s0898-1221(04)90053-3

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