Numerische Mathematik

, Volume 90, Issue 1, pp 1–18

Second order Chebyshev methods based on orthogonal polynomials

  • Assyr Abdulle
  • Alexei A. Medovikov

DOI: 10.1007/s002110100292

Cite this article as:
Abdulle, A. & Medovikov, A. Numer. Math. (2001) 90: 1. doi:10.1007/s002110100292


Stabilized methods (also called Chebyshev methods) are explicit Runge-Kutta methods with extended stability domains along the negative real axis. These methods are intended for large mildly stiff problems, originating mainly from parabolic PDEs. The aim of this paper is to show that with the use of orthogonal polynomials, we can construct nearly optimal stability polynomials of second order with a three-term recurrence relation. These polynomials can be used to construct a new numerical method, which is implemented in a code called ROCK2. This new numerical method can be seen as a combination of van der Houwen-Sommeijer-type methods and Lebedev-type methods.

Mathematics Subject Classification (1991): 65L20, 65M20

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Assyr Abdulle
    • 1
  • Alexei A. Medovikov
    • 2
  1. 1.Département de Mathématiques, Université de Genève, 1211 Genève 24, Switzerland; e-mail: Assyr.Abdulle@math.unige.chCH
  2. 2.Inst. of Numer. Math., Academy of Sciences, MoscowRU