A CLASS OF SECOND DERIVATIVES LINEAR MULTl-STEP METHOD FOR INTEGRATION OF STIFF FIRST ORDER INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

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.