Abstract: In this paper, a direct method based on variable step
size Block Backward Differentiation Formula which is referred as
BBDF2 for solving second order Ordinary Differential Equations
(ODEs) is developed. The advantages of the BBDF2 method over the
corresponding sequential variable step variable order Backward
Differentiation Formula (BDFVS) when used to solve the same
problem as a first order system are pointed out. Numerical results are
given to validate the method.
Abstract: 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.