5 research outputs found
Numerical treatment of first order delay differential equations using extended block backward differentiation formulae
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