This paper proposes a half-step third derivative hybrid block method with two cases of order four for solution of third Order Ordinary Differential Equations.Method of interpolation and collocation of power series approximate solution was used to generate the continuous hybrid linear multistep method,which was then evaluated at non-interpolating points to give a continuous block method. The discrete block method was recovered when the continuous block was evaluated at all step points. The basic properties of the method were investigated and were found to be zero-stable, consistent and convergent. The develop half-step method is applied to solve some third order initial value problems of ordinary differential equations and from the numerical results obtained, it is observed that our methods gives better approximation than the existing method compared with.

Keywords: Half-step, Hybrid Block Method, Third derivative. 65L05, 65L06, 65L20