The Computational Solution of First Order Delay Differential Equations Using Second Derivative Block Backward Differentiation Formulae

Abstract

In this paper, we implemented second derivative block backward differentiation formulae methods in solving first order delay differential equations without the application of interpolation methods in investigating the delay argument. The delay argument was evaluated using a suitable idea of sequence which we incorporated into some first order delay differential equations before its numerical evaluations. The construction of the continuous expressions of these of block methods was executed through the use of second derivative backward differentiation formulae method on the bases of linear multistep collocation approach using matrix inversion method to derive the discrete schemes. After the numerical experiments, the new proposed method was observed to be convergent, stable and less time consuming. From the numerical solutions obtained, the scheme for step number k = 4 performed better in terms of accuracy than that of the schemes for step numbers k = 3 and 2 when compared with other existing methods.

A Class of Seventh Order Hybrid Extended Block Adams Moulton Methods for Numerical Solutions of First Order Delay Differential Equations

“…In order to overcome the difficulty posed by using interpolation formula in computing the delay term, we shall apply the valid expression formulated by [8]. This approach has been successfully applied by [9,10,11,12,13,14,15] for numerical approximation of first order DDEs without applying interpolation formula in calculating the delay term.…”