3- Point Single Hybrid Block Method (3PSHBM) for Direct Solution of General Second Order Initial Value Problem of Ordinary Differential Equations

In this research article, a Three Point Single Hybrid Block Method for Direct solution of general second order ordinary differential equations is considered. The method was derived by collocation and interpolation of power series approximation to generate a continuous linear multistep method. The resultant method was evaluated at selected grid and off grid points to generate a discrete block method. The basic properties of the method such as order, error constant, zero Stability and consistency are investigated. The new method was tested on some numerical examples which ranges from linear, non-linear and real life problem of initial value problems and was found to be more efficient and give better approximation than the existing methods.