Thirty years of G-stability

The 1976 paper of G. Dahlquist, [13], has had a wide-ranging impact on our understanding of numerical methods for the solution of stiff differential equation systems. The present paper surveys some of the work of Dahlquist in this area. It also shows how this has led to contributions by other authors. In particular, the paper contains a review of non-linear stability for Runge–Kutta and general linear methods.

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[14]  John C. Butcher,et al.  The equivalence of algebraic stability andAN-stability , 1987 .

[15]  John C. Butcher.  Linear and non-linear stability for general linear methods , 1987 .

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[18]  Y. Suris,et al.  The canonicity of mappings generated by Runge-Kutta type methods when integrating the systems x¨ = - 6 U/ 6 x , 1989 .

[19]  J. M. Sanz-Serna,et al.  Symplectic integrators for Hamiltonian problems: an overview , 1992, Acta Numerica.

[20]  J. Butcher,et al.  Linear Multistep Methods as Irreducible General Linear Methods , 2006 .