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1 results

  • 21 - Stiff Systems of Ordinary Differential Equations and Linear Stability

  • from Part IV - Initial Value Problems for Ordinary Differential Equations
  • Abner J. Salgado, University of Tennessee, Knoxville, Steven M. Wise, University of Tennessee, Knoxville
  • Book:
    Classical Numerical Analysis
    Published online:
    29 September 2022
    Print publication:
    20 October 2022, pp 581-595

  • Summary

    The topic of this chapter is linear stability of schemes for ODEs. The notions of stiffness, linear stability domain, and A-stability are introduced. We discuss the A-stability of Runge-Kutta schemes via the amplification factor. The notion of A-acceptable, Pade approximations of the exponential, and the Hairer-Wanner-Norsett theorem are then presented. This allows us to show that all Gauss-Legendre-Runge-Kutta schemes are A-stable. For multistep schemes we present linear stability criteria and Dahlquist second barrier theorem. The boundary locus method concludes the chapter.