Abstract:
In this thesis, a class of second derivative Linear Multi-step methods for
integration of stiff initial value problem in ordinary differential equations
developed. The method is motivated by the second derivative method by Enright
(1972). The basic properties of the method, such as the order, error term, consistency
and stability were investigated. The methods are found to be consistent, stable and of
order k +2. The developed formula was computerised and implemented on a digital
computer to solve some sample initial value problems of Ordinary Differential
Equations. Numerical results show that the new method is accurate and compares
favourably with the existing second derivative method and Backward Difference
Formula respectively.
