References
- Cash , J. R. 1981 . High order P-stable formulae for numerical integration of periodic initial value problems . Numer. Math. , 37 : 355 – 370 .
- Chawla , M. M. 1981 . Two-step fourth order P-stable methods for second-order differential equation . BIT , 21 : 190 – 193 .
- Coleman , J. P. 1988 . Characterization of a class of P-stable methods for differential equations of second order . J. Comput. Appl. Math. , 22 : 137 – 141 .
- Coleman , J. P. 1989 . Numerical methods for y″ = f(x y) via rational approximations for the cosine . IMA J. of Numer. Anal. , 9 : 145 – 165 .
- Kramarz , L. 1980 . Stability of collocation methods for the numerical solution of y″ = f(x y) . BIT , 20 : 215 – 222 .
- Lambert , J. D. 1973 . Computational Methods in Ordinary Differential Equations , New York : Wiley .
- Lambert , J. D. and Watson , I. A. 1976 . Symmetric multistep methods for periodic initial value problems . J. Inst. Math. Appl. , 18 : 189 – 202 .
- Loscalzo , F. R. 1969 . “ An introduction to the application of spline functions to initial value problems ” . In Theory and Applications of Spline Functions , Edited by: Greville , T. N. E. 37 – 64 . New York : Academic Press .
- Norsett , S. P. 1984 . “ Splines and collocation for ordinary initial value problems ” . In Approximation Theory and Spline Functions , 397 – 417 . Dordrecht : Reidel .
- Sallam , S. and Karaballi , A. A. 1996 . A quartic C3-spline collocation method for solving second-order initial value problems . J. Comp. Appl. Math. , 75 : 295 – 304 .
- Simos , T. E. 1993 . Runge-Kutta-Nyström interpolants for the numerical integration of special second-order periodic initial-value problems . J. Comput. Math. Appl. , 26 : 7 – 15 .
- Simos , T. E. 1993 . Embedded Runge-Kutta methods for periodic initial-value problems . Math. Comput. Simul. , 35 : 387 – 395 .
- Twizell , E. H. and Khaliq , A. Q. M. 1984 . Multiderivative methods for periodic initial value problems . SIAM J. Numer. Anal. , 21 : 111 – 122 .
- Van Der Houwen , P. J. and Sommeijer , B. P. 1987 . Predictor-corrector methods for periodic second-order initial value problems . IMA J. Numer. Anal. , 7 : 407 – 422 .