On the A-Stability of Runge--Kutta Collocation Methods Based on Orthogonal Polynomials

Authors:
Roberto Barrio
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
1999

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Abstract

Some results about the A-stability of Runge--Kutta collocation methods based on the zeros and extrema of the ultraspherical or Gegenbauer polynomials are presented. These methods are implicit and the A-stability is an important property usually demanded. The Routh--Hurwitz algorithm is used to establish the main results about the A-stability of the methods, depending on the parameter $\lambda$ of the polynomials. For low degree methods some analytical results are presented, while for higher degree an open problem based on numerical tests is proposed.