Numerical solution of differential – difference equations having an interior layer using nonstandard finite differences

Abstract

This paper addresses the solution of a differential-difference type equation having an interior layer behaviour. A difference scheme is suggested to solve this equation using a non-standard finite difference method. Finite differences are derived from the first and second order derivatives. Using these approximations, the given equation is discretized. The discretized equation is solved using the algorithm for the tridiagonal system. The method is examined for convergence. Numerical examples are illustrated to validate the method. Maximum errors in the solution, in contrast to the other methods are organized to justify the method. The layer behaviour in the solution of the examples is depicted in graphs.

A Novel Numerical Scheme for a Class of Singularly Perturbed Differential-Difference Equations with a Fixed Large Delay

“…The author of [23] investigated a boundary value problem with the Sturm-Liouville type conditions using Green's function method for a linear ordinary differential equation of fractional order with delay. In [24], authors proposed a scheme for the solution of a differential equation with delay and advanced parameters having an interior layer behaviour using a non-standard finite difference method.…”