Explicit parallel two-step runge-Kutta-Nyström methods

Computers and Mathematics with Applications

Volumn 32, Issue 3, 1996, Pages 119-130

  Cong, N H ^a,b  

^a CWI   (Netherlands)

^b HANOI UNIVERSITY   (Viet Nam)

Author keywords

Parallelism; Predictor corrector methods; Runge Kutta Nystr m methods

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; ITERATIVE METHODS; NUMERICAL METHODS; OPTIMIZATION; RESOURCE ALLOCATION;

COLLOCATION METHOD; INITIAL VALUE PROBLEM; PARALLELISM; PREDICTOR CORRECTOR METHODS; RUNGE KUTTA NYSTROM METHODS; SECOND ORDER EQUATION;

PARALLEL PROCESSING SYSTEMS;

EID: 0030214508     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/0898-1221(96)00117-4     Document Type: Article

References (19)

1. E. Fehlberg, Klassische Runge-Kutta-Nyström Formeln mit Schrittweiten-Kontrolle für Differentialgleichungen x″ = f(t, x). Computing 10, 305-315 (1972).
2. E. Fehlberg, Eine Runge-Kutta-Nyström Formel 9-ter Ordnung mit Schrittweitenkontrolle für Differential-gleichungen x″ = f(t, x), Z. Angew. Math. Mech. 61, 477-485 (1981).
3. E. Hairer, Méthodes de Nyström pour !'équations différentielle y″(t) = f(t, y), Numer. Math. 27, 283-300 (1982).
4. E. Hairer, A one-step method of order 10 for y″ = f(x, y), IMA J. Numer. Anal. 2, 83-94 (1982).
5. N.h. Cong, Note on the performance of direct and indirect Runge-Kutta-Nyström methods, J. Comp. Appl. Math. 45, 347-355 (1993).
6. B.P. Sommeijer, Explicit, high-order Runge-Kutta-Nyström methods for parallel computers, Appl. Numer. Math. 13, 221-240 (1993).
7. P.J. van der Houwen, B.P. Sommeijer and N.h. Cong, Stability of collocation-based Runge-Kutta-Nyström methods, BIT 31, 469-481 (1991).
8. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, Applied Mathematics Series 55, National Bureau of Standards, Dover, New York, (1970).
9. P.J. van der Houwen and N.h. Cong, Parallel block predictor-corrector methods of Runge-Kutta type, Appl. Numer. Math. 13, 109-123 (1993).
10. N.h. Cong, Parallel iteration of symmetric Runge-Kutta methods for nonstiff problems, J. Comp. Appl. Math. (to appear).
11. S. Filippi and J. Gräf, Eine Runge-Kutta-Nyström Formelpaar der Ordnung 11(12) Differentialgleichungen der Form y″ = f(t, y), Computing 34, 271-282 (1985).
12. S. Filippi and J. Gräf, New Runge-Kutta-Nyström formula-pairs of order 8(7), 9(8), 10(9) and 11(10) for differential equations of the form y″ = f(t, y), J. Comp. Appl. Math. 14, 361-370 (1986).
13. L.F. Shampine and M.K. Gordon, Computer solution of ordinary differential equations, The Initial Value Problem, W.H. Freeman and Company, San Francisco, (1975).
14. E. Hairer, S.P. Nørsett and G. Wanner, Solving Ordinary Differential Equations, I. Nonstiff Problems, Springer-Verlag, Berlin, (1987).
15. E. Fehlberg, S. Filippi and J. Gräf, Eine Runge-Kutta-Nyström Formelpaar der Ordnung 10(11) für Differentialgleichungen y″ = f(t, y), Z. Angew. Math. Mech. 66, 265-270 (1986).
16. W. Glasmacher and D. Sommer, Implizite Runge-Kutta-Formeln, Westdeutscher Verlag, Köln, (1966).
17. P.J. van der Houwen, B.P. Sommeijer and N.h. Cong, Parallel diagonally implicit Runge-Kutta-Nyström methods, Appl. Numer. Math. 9, 111-131 (1992).
18. N.h. Cong, A-stable diagonally implicit Runge-Kutta-Nyström methods for parallel computers, Numerical Algorithms 4, 263-281 (1993).
19. N.h. Cong, Highly parallel predictor-corrector methods of Runge-Kutta-Nyström type, in preparation.