Abstract
Efficient families ofP-stable formulae are developed for the numerical integration of periodic initial value problems where the required solution has an unknown period. Formulae of orders 4 and 6 requiring respectively 2 and 4 function evaluations per step are derived and some numerical results are given.
Similar content being viewed by others
References
J. R. Cash,High order P-stable formulae for the numerical integration of periodic initial value problems, Numer. Math. 37 (1981), 355–370.
M. M. Chawla,Two-step fourth order P-stable methods for second order differential equations, BIT 21 (1981), 190–193.
M. M. Chawla, Private communication.
F. Costabile and C. Costabile,Two step fourth order P-stable methods for second order differential equations, BIT 22 (1982), 384–386.
G. Dahlquist,On accuracy and unconditional stability of linear multistep methods for second order differential equations, BIT 18 (1978), 133–136.
E. Hairer,Unconditionally stable methods for second order differential equations, Numer. Math. 32 (1979), 373–379.
J. D. Lambert and I. A. Watson,Symmetric multistep methods for periodic initial value problems, J. IMA, 18 (1976), 189–202.
E. Stiefel and D. G. Bettis,Stabilization of Cowell's methods, Numer. Math. 13 (1969), 154–175.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cash, J.R. EfficientP-stable methods for periodic initial value problems. BIT 24, 248–252 (1984). https://doi.org/10.1007/BF01937491
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01937491