Multistep Collocation Block Method for Direct Solution of Second Order Ordinary Differential Equations

In this study, block method of order six for solving second order ordinary differential equations is developed. The method of interpolation of approximated power series and collocation of its second derivative is adopted in the derivation of the method. The developed method is applied in block form to produce approximate solution at five points simultaneously. The stability properties of the method such as order, error constants, consistency and convergence are investigated. The developed method was then applied to solve some initial value problems of second order ordinary differential equations and the numerical results indicated that the new method produced better accuracy than the existing methods when solving the same problems.