Parallel Block Backward Differentiation Formulas for Solving Ordinary Differential Equations

A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I - hβJ . Here, J is the Jacobian matrix of the problem. In this paper, the matrix operations is paralleled in order to reduce the cost of the iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm.

Authors:

• Khairil Iskandar Othman
• Zarina Bibi Ibrahim
• Mohamed Suleiman

Keywords:

• Backward Differentiation Formula
• block
• ordinarydifferential equations.

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