37
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Variable step stiffly stable methods

&
Pages 227-240 | Received 05 Sep 1996, Accepted 22 Sep 1996, Published online: 19 Mar 2007

References

  • Alexander , R.K. 1994 . Stability of Runge-Kutta methods for stiff ordinary differential equations . SIAM J. Numer. Anal , 31 ( 4 ) : 1147 – 1168 .
  • Brayton , R.K. , Gustavson , F.G. and Hachtel , G.D. 1972 . A new efficient algorithm for solving differential – algebric systems using implicit backword difference formulas . Proc. IEEE , 60 : 98 – 108 .
  • Crouzeix , M. and Lisbona , F.J. 1984 . The convergance of variable– stepsize, variable-formula, multistep methods . SIAM J. Numer, Anal , 21 ( 3 ) : 512 – 534 .
  • Duffin , R.J. 1969 . Algorithms for classical stability problems . SIAM Review , 11 ( 2 ) : 196 – 213 .
  • Gear , C.W. 1971 . Numerical initial value problems in ordinary differential equations , Englewood Cliffs, N.J : Prentice Hall .
  • Gear , C.W. and Tu , K.W. 1974 . The effect of variable mesh size on the stability of multistep methods . SIAM J. Numer, Anal , 11 ( 5 ) : 1025 – 1043 .
  • Jeltsch , R. 1976 . Stiff stability and its relation to A 0– and ,A(0)–stability . SIAM. J. Numer. Anal , 13 ( 1 ) : 9 – 17 .
  • Linger , W. and Heights , Yorktown . 1968 . A criterion for A–stability of linear multistep integration formula . computing , 3 : 280 – 285 .
  • Hairer , E. and Wanner , G. 1991 . Solving ordinary differential equations II: Stiff and Differential – algebraic problems , Berlin : Springer .
  • Kreiss , H.O. and Lixin , Wu . 1993 . On the stability definition of difference approximations for the initial boundary value problem . Applied Numerical Mathematics , 12 : 213 – 227 .
  • Lambert , J.D. 1991 . Numerical Methods for ordinary differential systems: The initial value problem , New York : John Wiley .
  • Piotrowski , P. . Stability, consistency and convergence of variable k-step methods for numerical integration of large systems of ordinary differential equations . Conference on the numerical solution of differential equations . pp. 221 – 227 . Berlin : Springer .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.