Various types of methods have been developed for solving the
special second order ODEs which is not explicitly dependent on the
first derivative of the solution. The solution to the equation can
be obtained by reducing it to an equivalent first order system of
twice the dimension and solved using a standard numerical methods.
However it is often advantageous to solve them directly. This book
focused on the derivation of the block methods for solving the
special second order ODEs directly. The early section of the book
is devoted to the derivation of the methods using linear operator.
Then the derivation of the method is done using Newton-Gregory
backward interpolation formula. Numerical results of the methods
are compared with the existing methods which shows that they are
computationally more efficient. Block methods are suitable for
parallel implementation, hence parallel codes of the methods are
developed for solving large systems of ODEs. The performance of the
methods using sequential and parallel codes are compared which
clearly shows that the parallel codes produced better speedup and
efficiency.
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