Some Uniform Order Block Methods for the Solution of First Order Ordinary Differential Equations

Abstract

In this Paper, we consider the derivation of a continuous formulation of a linear multistep method for ordinary differential equations by collocation methods without the use of predictor-corrector approach. All the discrete schemes used in each of the block method at k=2 and k=3 derived, come from a single continuous formulation and its derivative. The block suggested approach is self-starting and produce parallel solution of the ordinary differential equations (ODES) which minimizes the cost of computation compared to other variants. Both block methods at k=3 and k=2 converges to the exact solutions with the two Numerical examples tested with this approach.

Keywords: Uniform order, Block methods, first order odes, initial value problem, self starting and parallel solutions

Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 149 - 154