Numerical Simulation for a Differential Difference Equation With an Interior Layer - Amala, P.; Lalu, M.; Phaneendra, K. (Communications in Mathematics and Applications, 2023)
This paper addresses the solution of a differential-difference type equation having an interior layer behaviour. An approach is suggested to solve this equation using a numerical integration scheme and linear interpolation. Taylor expansions are utilized to handle the shift arguments. In order to solve the discretized equation, the tridiagonal solver is applied. The approach is analyzed for convergence. Numerical examples are demonstrated to validate the scheme. Maximum errors in the solution, in contrast to the other methods, are organized to explain the approach. The layer profile in the solutions of the examples is illustrated in graphs.
Keywords: Differential-difference equation; Numerical integration; Layer behaviour; Convergence