Difference Scheme for Differential-Difference Problems with Small Shifts Arising in Computational Model of Neuronal Variability

Abstract

The solution of differential-difference equations with small shifts having layer behaviour is the subject of this study. A difference scheme is proposed to solve this equation using a non-uniform grid. With the non-uniform grid, finite - difference estimates are derived for the first and second-order derivatives. Using these approximations, the given equation is discretized. The discretized equation is solved using the tridiagonal system algorithm. Convergence of the scheme is examined. Various numerical simulations are presented to demonstrate the validity of the scheme. In contrast to other techniques, maximum errors in the solution are organized to support the method. The layer behaviour in the solutions of the examples is depicted in graphs.

Keywords

• non-uniform grid
• differential-difference equation
• boundary layer