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.