Modified SDBDF Based on a Non-Zero Root of the Second Characteristics Polynomial

Abstract

The second derivative backward differentiation formulas (SDBDF) are
well known for the integration of stiff initial value problems. In this
paper, a class of second derivative linear multistep method (SDLMM) is
proposed based on the modification of SDBDF. The proposed class of
methods which allows a root of the second characteristics polynomial to
be within the unit disc but not at the origin. The class of methods is -
stable for order 4 and -stable up to order . Numerical
examples are presented to show the application of the proposed methods
in the integration of IVPs in ODEs. The results however showed that
methods proposed are good integrators in the treatment of stiff problems.