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

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.

Authors:

• Zarina Bibi
• I.
• Khairil Iskandar
• O.

Keywords:

• Ordinary differential equations
• parallel.

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.