Three-step Four-point Optimized Hybrid Block Method for Direct Solution of General Third Order Differential Equations

Abstract

This research work considers derivation of three step four point optimized hybrid block method for solving general third order 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 the general third order ode problems. Continuous linear multistep method is developed by interpolating the basis function at both grid and off-grid points and collocating the differential function at only grid points. The unknown parameters in the system of linear equations arising from the collocation and interpolation functions were determined and the values substituted in the approximate solution to the problem. The required continuous method is obtained after necessary simplification. The derived method is tested and found to be consistent, symmetric and of low error constant. The results obtained showed a better performance than the existing methods in literature under review.