New developed numerical formula for solution of first and higher order ordinary differential equations

Solutions of first, second and third order ordinary differential equations via new developed numerical scheme is studied in this article. The derivation of this novel numerical method is achieved by the use of interpolation and collocation approach where power series approximate is taken to be interpolating polynomial while its derivatives as collocating equations. A class of numerical methods that form the block is derived by evaluating non-interpolating points within the interval of integration. The order of the block is found to be twelve which established the consistency of the scheme. Its efficiency is examined on some first, second and third order initial value problems as well as real life problems, the generated numerical results displayed on Tables 1 - 6 reveal the effectiveness and accuracy of the new developed block method over current methods in terms of error.