Egwu, Bernard Anuga.2023-12-142023-12-142019-11-20A DISSERTATION SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES, NASARAWA STATE UNIVERSITY IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF MASTERS DEGREE (M.SC) IN MATHEMATICShttps://keffi.nsuk.edu.ng/handle/20.500.14448/5788ith initial value conditions using extrapolation of continuous linear multistep methods. By this we mean using the same numerical methods to approximate numerically the solution of an initial value problem (IVP). For example, a problem is to be solved in the interval say [a, b], our interest is to solve the problem / find the solution at a point outside the boundary of the interval to the right say without doing any further calculation with those methods. What we want to solve in this problem is using the continuous linear multistep methods for their evaluations outside their range of construction. If the solution is valid within the interval and you are interested in the validity of the solution outside the interval is called extrapolation. Our studies show that the continuous formula can be used to finding values outside the interval of consideration which the discrete formula cannot do. Our studies also compare the results of continuous linear multistep methods and the discrete scheme with the exact solution and discovered that the continuous scheme minimizes the error which is better.esThesis