Stability of Chebyshev collocation methods

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.