Order four continuous hybrid block method for the solutions of second order ordinary differential equations

Abstract

We consirdered method of collocation of the differential system and interpolation of the approximate solution to generate a continuous hybrid linear multistep method, which is solved for the independent solution to give a continuous block method. The resultant method is evaluated at selected grid points to generate a discrete block method. The basic properties of the method was investigated and found to be zero stable, consistent and convergent. The method was tested on some numerical examples and found to compete favourably with the existing methods.