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.
In this study, numerical solution of a differential-difference equation with a boundary layer at one end of the domain is suggested using an exponential spline. The numerical scheme is developed using an exponential spline with a special type of mesh. A fitting parameter is inserted in the scheme to improve the accuracy and to control the oscillations in the solution due to large delay. Convergence of the method is examined. The error profiles are represented by tabulating the maximum absolute errors in the solution. Graphs are being used to show that how the fitting parameter influence the layer structure.
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