keywords: Block method, higher order ODE, interpolation, collocation, power series
Our focus in this research is to developed block method for solving higher order ordinary differential equation using power series on implicit one-step. In order to achieve the aim and objective of this research, we used interpolation, collocation and evaluate a power series approximation at some chosen grid and off-grid points to generate an implicit continuous hybrid one-step method. As requirement of any numerical analyst, the properties of one-step block method was done and results showed that it is consistent, convergent, zero stable and with region of absolutely stable. The method was tested with numerical examples solved using the existing methods and our method was found to give better results when compared with the existing method. Obviously, the solution graphs show the convergence of the method with exact solutions.