We consider collocation and interpolation of the approximate solution at some selected grid and off grid points to give a system of nonlinear equations, solving for the unknown constants using Guassian elimination method and substituting into the approximate solution gives the continuous block method. We investigate the basic properties of the derived method, numerical examples show that the method is suitable for solving fourth order initial value problem of ordinary differential equations.

This paper discussed the development of one -step, one hybrid block method for the solution of first order initial value problems. Two functions were combined to form the basis function which is collocated and interpolated at some selected grid and off-grid points to develop a linear multistep method which is implemented in block form. The paper further investigated the properties of the block method and found it to be convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to give better approximation than the methods we compared our results with.

We introduce one step continuous Runge Kutta collocation method with three free parameters for the solution of stiff first order ordinary differential equations. We adopt interpolation and collocation of the approximate solution at some selected grid points to give system of non linear equations. Using Crammer's rule to solve for the unknown parameters and substituting into the approximate solution gives the continuous method. To determine how best to fix the free parameters, we consider