References

Bendtsen, C., 1997. ParSodes: A Parallel Stiff ODE Solver. Version 1.0, UNIC, Technical University of Denmark, Bldg, Denmark.

Brown, P.N., G.D. Byrne and A.C. Hindmarsh, 1989. VODE, a variable-coefficient ODE solver. SIAM J. Scient. Statist. Comput., 10: 1038-1051.
CrossRef  |  

Burrage, K., 1995. Parallel and Sequential Methods for Ordinary Differential Equations. Numerical Mathematics and Scientific Computation Series. Oxford University Press, New York,.

Byrne, G.D., 1992. Pragmatic Experiments with Krylov Methods in the Stiff ODE Setting. In: Computational Ordinary Differential Equations, Cash, J.R. and I. Gladwell (Eds.). Oxford University Press, Oxford, pp: 323-356.

Cohen, S.D. and A.C. Hindmarsh, 1994. CVODE user guide. Numerical Mathematics Group, UCRL-MA-118618.

Cohen, S.D. and A.C. Hindmarsh, 1996. CVODE, A stiff/nonstiff ODE solver in C. Comput. Physics, 10: 138-143.

De Swart, J.J.B., W.M. Lioen and W.A. van der Veen, 1998. Parallel stormer-cowell methods for high-precision orbit computations. Applied Numerical Mathematics, 31: 353-374.
CrossRef  |  

Dormand, J.R., J.P. Gilmore and P.J. Prince, 1994. Globally embedded Runge-Kutta schemes. Ann. Numer. Mathe., 1: 97-106.

Fengqi, Y., W. Junjie and S. Junping 2008. Diffusion-driven instability and bifurcation in the lengyel-epstein system. Nonlinear Anal. Real World Appl., 9: 1038-1051.
CrossRef  |  

Geist, A., A. Beguelin, J. Dongarra, W. Jiang, R. Manchek and V.S. Sunderam, 1994. PVM: Parallel Virtual Machine: A Users Guide and Tutorial for Networked Parallel Computing. MIT Press, Massachusetts, Cambridge, ISBN: 0-262-57108-0.

Hairer, E., S.P. Norsett and G. Wanner, 1993. Solving Ordinary Differential Equations I: Nonstiff Problems. 2nd Edn., Springer-Verlag, Berlin, Heidelberg, ISBN: 978-3-540-56670-0.

Iserles, A. and S.P. Norsett, 1990. On the theory of parallel Runge-Kutta methods. IMA J. Numer. Anal., 10: 463-488.
CrossRef  |  

Kartawidjaja, M.A., 2004. Performance of parallel ODE solver using semi-implicit runge-kutta method. http://lontar.cs.ui.ac.id/Lontar/opac/themes/ng/hasilcari.jsp?method=similar&query=8609&lokasi=lokal.

Kartawidjaja, M.A., H. Suhartanto and T. Basaruddin, 2004. Performance of a parallel technique for solving nonlinear systems arising from ODEs. IEEE. TenCon, Chiang Mai, Thailand, 4: 403-406.

Kartawidjaja, M.A., H. Suhartanto and T. Basaruddin, 2004. Performance of parallel iterative solution of linear systems using GMRES. http://kopaonik.internetconferences.net/BookOfAbstractsBody.doc.

Merson, R.H., 1957. An Operational Method for the Study of Integration Processes. Weapons Research Establishment, Salisbury, South Australia.

Saad, Y. and M.H. Schultz, 1986. A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput., 7: 856-869.

Skeel, R.D., 1986. Thirteen ways to estimate global error. Numerische Mathematik, 48: 1-20.
CrossRef  |  

Soderlind, G., 2003. Digital filters in adaptive time-stepping. ACM Trans. Mathe. Software, 29: 1-26.

Suhartanto, H., 2007. VSMRK: A parallel implementation and the performance of variable stepsize multistep Runge-Kutta methods for stiff ODEs. Asian J. Inform. Technol., 6: 1110-1116.

Wu, X., 1999. Performance Evaluation, Prediction and Visualization of Parallel Systems. Kluwer Academic Publishers, The Netherlands, ISBN: 0-7923-8462-8.