A New Implicit Block Method for Solving Second Order Ordinary Differential Equations Directly

This article considers the derivation of an implicit block method for the solution of initial value problems of ordinary differential equations directly. The method of interpolation and collocation is adopted in developing the method where approximated power series of the form y(x) = Sigma(k+2)(j=0)a(j)x(j) is used as an interpolation polynomial and its second derivative is collocated at the selected grid points where k=5. The method developed is zero stable, consistent and convergent. The generated numerical results show that the new method is better when compared with the existing methods of the same step-length in terms of error.