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

摘要

> >Inthis study, block method of order six for solving second order ordinarydifferential equations is developed. The method of interpolation ofapproximated power series and collocation of its second derivative is adoptedin the derivation of the method. The developed method is applied in block formto produce approximate solution at five points simultaneously. The stabilityproperties of the method such as order, error constants, consistency andconvergence are investigated. The developed method was then applied to solve some initialvalue problems of second order ordinary differential equations and thenumerical results indicated that the new method produced better accuracy thanthe existing methods when solving the same problems.