Numerical treatment of first order delay differential equations using extended block backward differentiation formulae

Abstract

In this research, we developed and implemented extended backward differentiation methods (formulae) in block forms for step numbers k = 2, 3 and 4 to evaluate numerical solutions for certain first-order differential equations of delay type, generally referred to as delay differential equations (DDEs), without the use of interpolation methods for estimating the delay term. The matrix inversion approach was applied to formulate the continuous composition of these block methods through linear multistep collocation method. The discrete schemes were established through the continuous composition for each step number, which evaluated the error constants, order, consistency, convergent and area of absolute equilibrium of these discrete schemes. The study of the absolute error results revealed that, as opposed to the exact solutions, the lower step number implemented with super futures points work better than the higher step numbers implemented with super future points.