Numerical solutions of first order delay differential equations using second derivative block Adams Moulton Methods

Résumé

In this paper, we formulated and applied Second Derivative Block Adams Moulton Methods in solving first order delay differential equations without the introduction of interpolation formula in evaluating the delay argument. The delay argument was evaluated by applying an acceptable idea of sequences. The continuous forms of these of block methods were worked-out through the use
of linear multistep collocation procedure using matrix inversion approach. The resulting discrete schemes obtained from the various continuous expressions of the block methods were observed to be self-starting, consistent, zero-stable, convergent and satisfying region of P −and Q−stabilities. From the results obtained, the scheme for step number k = 4 performed better than the schemes for step numbers k = 3 and 2 in terms of accuracy when compared with their exact results.