2 – Block 3 - Point Modified Numerov Block Methods for Solving Ordinary Differential Equations

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations of the form y′′ f x, y , a x b with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different three discrete schemes, each of order (4,4,4), which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on linear and non-linear ordinary differential equations whose solutions are oscillatory or nearly periodic in nature, and the results obtained compared favourably with the exact solution. Keywords—Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.