A THREE-STEP SIMPSON'S TYPE EXPONENTIALLY-FITTED BACKWARD DIFFERENCE METHOD FOR THE NUMERICAL SOLUTION OF FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

A THREE-STEP SIMPSON'S TYPE EXPONENTIALLY-FITTED

Abstract

In this paper, a class of exponential fitting back-
ward dierence method (EFBDM) is derived for numerically
solving general frst order ordinary dierential equations. This
class of method is from the linear multistep method (LMM)
derived via the technique of collocation. The power series poly-
nomials used as basis function is fitted with an exponential func-
tion term. This class of EFBDM is derived for the step num-
ber k=3. The method satisfies the basic features of numerical
scheme which includes consistency and zero-stability. The con-
vergence of the method is also established. This class of 3-step
method is compared to already existing methods in literature to
establish its eciency in terms of global errors nd they compare
favourably with the methods cited.