Quintic C2 -spline integration methods for solving second-order ordinary initial value problems

Journal of Computational and Applied Mathematics

Volumn 115, Issue 1-2, 2000, Pages 495-502

  Sallam, S ^a   Anwar, M Naim ^a  

^a KUWAIT UNIVERSITY   (Kuwait)

Author keywords

56D05; 65L06; Absolute stability; Collocation method; Periodic stability; Quintic spline; Second order initial value problem

Indexed keywords

EID: 0004906061     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00174-0     Document Type: Article

References (12)

1. Chawla M.M. Numerov made explicit has better stability. BIT. 24:1984;117-118.
2. Chawla M.M., Al-Zanaidi M.A. A two-stage fourth-order "almost" P -stable method for oscillatory problems J. Comput. Appl. Math. 89:1998;115-118.
3. Coleman J.P. Numerical methods for. y″=f(x,y) via rational approximations for the cosine IMA J. Numer. Anal. 9:1989;145-165.
4. Franco J.M., Palacios M. High-order. P -stable multi-step methods J. Comput. Appl. Math. 30:1990;1-10.
5. E. Hairer, S.P. N ø rsett, G. Wanner, Solving ordinary differential equations I, Nonstiff Problems, Springer, Berlin, 1978.
6. Kirchgraber U. Multi-step methods are essentially one-step methods. Numer. Math. 48:1986;85-90.
7. Kramarz L. Stability of collocation methods for the numerical solution of. y″ = f(x,y) BIT. 20:1980;215-222.
8. (2) = f(x,y) with spline functions Math. Comp. 27:1973;807-816.
9. S.P. N ø rsett, Splines and collocation for ordinary initial value problems, in: S.P. Singh et al. (Eds.), Approximation Theory and Spline Functions, Reidel, Dordrecht, 1984, pp. 397-417.
10. 3 -spline collocation method for solving second-order initial value problems J. Comput . Appl. Math. 75:1996;295-304.
11. Sommeijer B.P. A note on a diagonally implicit Runge-Kutta-Nyström method. J. Comput. Appl. Math. 19:1987;395-399.
12. Van der Houwen P.J., Sommeijer B.P. Explicit Runge-Kutta-Nyström methods with reduced phase errors for computing oscillating solutions. SIAM J. Numer. Anal. 24:1987;595-617.