Abstract:
Due to the wider applications of singularly perturbed differential equation (SPDDEs)
in the real life problems, there has been growing interest to develop numerical methods
for SPDDEs. However, as the perturbation parameter decreases in magnitude, standard
numerical methods for solving singularly perturbed differential equations are unstable,
inefficient and inaccurate. Thus, it is pretty reasonable to construct numerical meth
ods whose convergence properties, accuracy and the computation cost are independent
of the value of the perturbation parameter. One of the approaches to derive-uniform
convergent numerical methods for solving SPDDEs is through the application of fitted op
erator method which can be constructed by using either exponentially fitted operator or
non-standard finite difference methods. The design of the non-standard finite difference
methods (NSFDMs) starts mostly with the concept of exact schemes. A major advantage
of having an exact difference scheme for a differential equation is that questions related
to the usual considerations of consistency, stability and convergence do not arise. The
objective of this project is, therefore, to construct-uniform convergent non-standard finite
difference method for solving singularly perturbed two parameter delay differential equa
tion using finite difference method. The convergence analysis and stability of the proposed
method will also be established.
