A quartic C3-spline collocation method for solving second-order initial value problems

Journal of Computational and Applied Mathematics

Volumn 75, Issue 2, 1996, Pages 295-304

  Sallam, S ^a   Karaballi, A A ^a  

^a KUWAIT UNIVERSITY   (Kuwait)

Author keywords

Absolute stability; Collocation methods; Numerov method; Periodic stability; Quartic spline

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS; PROBLEM SOLVING;

ABSOLUTE STABILITY; COLLOCATION METHODS; NUMEROV METHOD; PERIODIC STABILITY; QUARTIC SPLINES;

BOUNDARY VALUE PROBLEMS;

EID: 0030285138     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(96)00082-9     Document Type: Article

References (22)

1. J.R. Cash, High order P-stable formulae for numerical integration of periodic initial value problems, Numer. Math. 37 (1981) 355-370.
2. M.M. Chawla, Two-step fourth order P-stable methods for second-order differential equation, BIT 21 (1981) 190-193.
3. M.M. Chawla, Numerov made explicit has better stability, BIT 24 (1984) 117-118.
4. M.M. Chawla and P.S. Rao, A Noumerov-type method with minimal phase-lag for the integration of second-order initial-value problems, J. Comput. Appl. Math. 11 (1984) 277-281.
5. J.P. Coleman, Characterization of a class of P-stable methods for differential equations of second order, J. Comput. Appl. Math. 22 (1988) 137-141.
6. J.P. Coleman, Numerical methods for y″ = f(x, y) via rational approximations for the cosine, IMA J. Numer. Anal. 9 (1989) 145-165.
7. P. de Oliveira, On a class of multistep method with strong contractivity properties, J. Comput. Appl. Math. 30 (1992) 11-19.
8. S.O. Fatunla, Numerical Methods for Initial Value Problems in Ordinary Differential Equations (Academic Press, London, 1988).
9. J.M. Franco and M. Palacios, High-order P-stable multistep methods, J. Comput. Appl. Math. 30 (1990) 1-10.
10. E. Hairer, S.P. Norsett and G. Wanner, Solving Ordinary Differential Equations, Nonstiff Problems (Springer, Berlin, 1987).
11. L. Kramarz, Stability of collocation methods for the numerical solution of y″ = f(x, y), BIT 20 (1980) 215-222.
12. J.D. Lambert, Computational Methods in Ordinary Differential Equations (Wiley, New York, 1973).
13. J.D. Lambert and I.A. Watson, Symmetric multistep methods for periodic initial value problems, J. Inst. Math. Appl. 18 (1976) 189-202.
14. F.R. Loscalzo, An introduction to the application of spline functions to initial value problems, in: T.N.E. Greville, Ed., Theory and Applications of Spline Functions (Academic Press, New York, 1969) 37-64.
15. M. Meneguette, Chawla-Numerov method revisited, J. Comput. Appl. Math. 36 (1991) 247-250.
16. (2) = f(x, y) with spline functions, Math. Comp. 27 (1973) 807-816.
17. S.P. Norsett, Splines and collocation for ordinary initial value problems, in: S.P. Singh et al. Eds., Approximation Theory and Spline Functions (Reidel, Dordrecht, 1984) 397-417.
18. T.E. Simos, Runge-Kutta-Nyström interpolants for the numerical integration of special second-order periodic initial-value problems, J. Comput. Math. Appl. 26 (1993) 7-15.
19. T.E. Simos, A family of two-step almost P-stable methods with phase-lag of order infinity for the numerical integration of second-order periodic initial-value problems, Japan. J. Indust. Appl. Math. 10 (1993) 289-297.
20. T.E. Simos, Embedded Runge-Kutta methods for periodic initial-value problems, Math. Comput. Simulation 35 (1993) 387-395.
21. E.H. Twizell and A.Q. Khaliq, Multiderivative methods for periodic initial problems, SIAM J. Numer. Anal. 21 (1984) 111-122.
22. P.J. van der Houwen and B.P. Sommeijer, Predictor-corrector methods for periodic second-order initial value problems, IMA J. Numer. Anal. 7 (1987) 407-422.