New Zero-stable Block Method for Direct Solution of Fourth Order Ordinary Differential Equations

A zero-stable block method for solving fourth order initial value problems of ordinary differential equations directly is proposed. Interpolation and collocation techniques are employed in developing the method. Power series approximate is used as a basis function where its fourth derivative is collocated at all the grid points within the specified interval. Furthermore, the properties of the method developed, that is, zero-stability, consistency, convergence, order and error constant are established. The new method performs better than the existing methods in terms of accuracy.