Abstract
When a linear multistep method is used to solve a stiff differential equationy′(x)=f(y(x)), producing an approximationy n toy(x n ), it is preferable to approximate the valuey′(x n ) in subsequent formulae by a value which exactly satisfies the corrector equation used, rather than by the valuef(y n ). We prove that the resulting method is stable if the underlying corrector equation is absolutely stable, provided that the residuals obtained in solving successive nonlinear equations remain uniformly bounded.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. W. Gear and Y. Saad,Iterative solution of linear equations in ODE codes, SIAM J. Sci. Stat. Comp. 4 (1983), 583–601.
J. D. Lambert,Computational Methods in Ordinary Differential Equations, Wiley, New York (1973).
H. H. Robertson and J. Williams,Some properties of algorithms for stiff differential equations, JIMA 16 (1975), 23–34.
L. F. Shampine,Evaluation of implicit formulas for the solution of ODE's., BIT 19(1979), 495–502.
L. F. Shampine,Implementation of implicit formulas for the solution of ODE's., SIAM J. Sci. Stat. Comp. 1(1980), 103–118.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ypma, T.J. Linear stability of stiff differential equation solvers. BIT 24, 394–396 (1984). https://doi.org/10.1007/BF02136041
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02136041