A CLASS OF 4-POINT HYBRID METHODS FOR THE SOLUTION OF GENERAL THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

This research work considers the solution of third order initial value problems of ordinary differential equations (odes) without reduction to systems of lower order odes. A combination of power series and exponential function is used as an approximate solution to general third order problems. Continuous linear multistep methods of various stepnumbers (k) were developed by interpolating the basis function at both grid and off-grid points and collocating the differential function at only grid points. Collocation of the differential function at only grid points is aimed at reducing the functions evaluation. The unknown parameters in the system of linear equations arising from the collocation and interpolation procedures were determined and the values substituted in the approximate solution to the problem. The required continuous methods were obtained for different stepnumbers after necessary simplification. The derived methods were tested and found to be consistent, symmetric and of low error constants. The discrete schemes obtained from the continuous methods were implemented in Predictor-Corrector and also in Block modes. The results obtained showed better performance than some existing methods in literature under review.