Numerical experiments with some explicit pseudo two-step RK methods on a shared memory computer

Computers and Mathematics with Applications

Volumn 36, Issue 2, 1998, Pages 107-116

  Cong, N H ^a   Podhaisky, H ^b   Weiner, R ^b  

^a VIETNAM NATIONAL UNIVERSITY   (Viet Nam)

^b MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

Author keywords

Parallelism; Pseudo two step Runge Kutta methods; Runge Kutta methods

Indexed keywords

CODES (SYMBOLS); COMPUTERS; INITIAL VALUE PROBLEMS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; PARALLEL PROCESSING SYSTEMS; PROBLEM SOLVING;

PSEUDO TWO STEP RUNGE-KUTTA METHODS; SHARED MEMORY COMPUTER;

RUNGE KUTTA METHODS;

EID: 0032121074     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(98)00121-7     Document Type: Article

References (22)

1. J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations, Runge-Kutta and General Linear Methods, Wiley, New York, (1987).
2. E. Hairer, S.P. Nørsett and G. Wanner, Solving Ordinary Differential Equations, I. Nonstiff Problems, 2nd edition, Springer-Verlag, Berlin, (1993).
3. K. Burrage, Efficient block predictor-corrector methods with a small number of corrections, J. Comput. Appl. Math. 45, 139-150, (1993).
4. K. Burrage, Parallel methods for initial value problems, Appl. Numer. Math. 11, 5-25, (1993).
5. K. Burrage and H. Suhartanto, Parallel iterated methods based on multistep Runge-Kutta methods of Radau type, Advances in Computational Mathematics 7, 37-57, (1997).
6. M.T. Chu and H. Hamilton, Parallel solution of ODE's by multi-block methods, SIAM J. Sci. Statist. Comput. 8, 137-157, (1987)).
7. N.H. Cong, Parallel iteration of symmetric Runge-Kutta methods for nonstiff initial-value problems, J. Comput. Appl. Math. 51, 117-125, (1994).
8. N.H. Cong and T. Mitsui, A class of explicit parallel two-step Runge-Kutta methods, Japan J. Indust. Appl. Math. 14, 303-313, (1997).
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. P.J. van der Houwen and B.P. Sommeijer, Parallel iteration of high-order Runge-Kutta methods with stepsize control, J. Comput. Appl. Math. 29, 111-127, (1990).
11. P.J. van der Houwen and B.P. Sommeijer, Block Runge-Kutta methods on parallel computers, Z. Angew. Math. Mech. 68, 3-127, (1992).
12. K.R. Jackson and S.P. Nørsett, Parallel Runge-Kutta methods, Manuscript, (1988).
13. I. Lie, Some aspects of parallel Runge-Kutta methods, In Report No. 3/87, Division Numerical Mathematics, University of Trondheim, Norway, (1987).
14. S.P. Nørsett and H.H. Simonsen, Aspects of parallel Runge-Kutta methods, In Numerical Methods for Ordinary Differential Equations, Proceedings L'Aquilla 1987, Lecture Notes in Mathematics, 1386, (Edited by A. Bellen, C.W. Gear and E. Russo), Springer-Verlag, Berlin, (1989).
15. N.H. Cong, Explicit pseudo two-step Runge-Kutta methods for parallel computers, (submitted).
16. N.H. Cong, Continuous variable stepsize explicit pseudo two-step RK methods, (submitted).
17. K. Burrage and B. Pohl, Implementing an ODE code on distributed memory computers, Computers Math. Applic. 28 (10-12), 235-252, (1994).
18. K. Burrage, Parallel and Sequential Methods for Ordinary Differential Equations, Clarendon Press, Oxford, (1995).
19. M. Hochbruck, C. Lubich and H. Selhofer, Exponential integrators for large systems of differential equations, In Tech. Rept., Mathematisches Institut, Universität Tübingen, Germany, (1995).
20. R. Weiner, B.A. Schmitt and H. Podhaisky, ROWMAP - A ROW-code with Krylov techniques for large stiff ODEs, Appl. Numer. Math. 25, 1-16, (1997).
21. T.E. Hull, W.H. Enright, B.M. Fellen and A.E. Sedgwick, Comparing numerical methods for ordinary differential equations, SIAM J. Numer. Anal. 9, 603-637, (1972).
22. H. De Meyer, M. Van Daele and G. Vanden Berghe, On the implementation of parallel iterated Runge-Kutta methods on a transputer network, Appl. Numer. Math. 13, 155-163, (1993).