Parallel Block Backward Differentiation Formulas For Solving Large Systems of Ordinary Differential Equations

Authors: Zarina Bibi, I., Khairil Iskandar, O.

Abstract:

In this paper, parallelism in the solution of Ordinary Differential Equations (ODEs) to increase the computational speed is studied. The focus is the development of parallel algorithm of the two point Block Backward Differentiation Formulas (PBBDF) that can take advantage of the parallel architecture in computer technology. Parallelism is obtained by using Message Passing Interface (MPI). Numerical results are given to validate the efficiency of the PBBDF implementation as compared to the sequential implementation.

Keywords: Ordinary differential equations, parallel.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1058515

References:

[1] Bellen, A. and Zennaro, M. (1989), Parallel algorithms for initial value problems, J. Comput. Appl. Math., 25,pp. 341-350.
[2] Chu, M. & Hamilton, H. (1987), Parallel solution of ODEs by multi-block methods, SIAM J. Sci. Statist. Comput., 8, pp. 342-353.
[3] Gear, C.W. (1987), Parallel Methods For Ordinary Differential Equations, Report No. UIUCDCS-R-87-1369.
[4] Franklin, M., (1978). Parallel solution of ordinary differential equations, IEEE Trans. Comput., C-27, pp. 413-420.
[5] Hull, T.E., Enright, W.H., Fellen, B.M. and Sedgwick, A.E. (1972), Comparing Numerical Methods for Ordinary Differential Equations. Siam J. Num. Anal. 9(4):603-637.
[6] Ibrahim,Z.B., Suleiman, M.B., Othman, K.I., (2008). Fixed Coefficients Block Backward Differentiation Formulas for the Numerical Solution of Stiff Ordinary Differential Equations, European Journal of Scientific Research, Vol. 21 No.3, pp. 508-520.
[7] Nicolis G, Prigogine I. (1977), Self-organization in non-equilibrium systems. New York: Wiley-Interscience.
[8] Prigogine I, Lefever R. (1968), Symmetries breaking instabilities in dissipative systems II. Journal of Physical Chemistry; 48: 1695-1700.