Nonlinear stability of multistep multiderivative methods

@article{Li1990NonlinearSO,
  title={Nonlinear stability of multistep multiderivative methods},
  author={Shoufu Li and Baogen Ruan},
  journal={Mathematics of Computation},
  year={1990},
  volume={55},
  pages={581-589}
}
  • Shoufu Li, B. Ruan
  • Published 13 January 1990
  • Mathematics
  • Mathematics of Computation
In this paper we examine nonlinear stability of multistep multiderivative methods for initial value problems of a class K(, in a Banach space. Stability criteria are established which extend results of R. Vanselow to this class of methods. 
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References

SHOWING 1-9 OF 9 REFERENCES
Nonlinear stability behaviour of linear multistep methods
For linear multistep methods sufficient conditions are derived such that the numerical solutions of stable nonlinear initial value problems in Banach spaces are also stable.
Non-linear stability of multivalue multiderivative methods
In Burrage and Butcher [2] a stability property suitable for modelling non-linear ordinary differential equation problems was introduced for the family of general linear methods. In the present paper
A stability property of implicit Runge-Kutta methods
A class of implicit Runge-Kutta methods is shown to possess a stability property which is a natural extension of the notion ofA-stability for non-linear systems.
Non-linear stability of a general class of differential equation methods
TLDR
For a class of methods sufficiently general as to include linear multistep and Runge-Kutta methods as special cases, a concept known as algebraic stability is defined, based on a non-linear test problem, which enables estimates of error growth to be provided.
Stability Criteria for Implicit Runge–Kutta Methods
A comparison is made of two stability criteria. The first is a modification to nonautonomous problems of A-stability and the second is a similar modification of B-stability. It is shown that under
Contractive methods for stiff differential equations Part II
An integration method for ordinary differential equations is said to be contractive if all numerical solutions of the test equationx′=λx generated by that method are not only bounded (as required for
Numerical integration of ordinary differential equations based on trigonometric polynomials
There are many numerical methods available for the step-by-step integration of ordinary differential equations. Only few of them, however, take advantage of special properties of the solution that