A Numerical Approach To SPDDE Via Fitted Scheme

Abstract

A fitted scheme is to solve the singularly perturbed differential-difference equations. The considered equation is first reduced to the ordinary singularly perturbed problem by expanding the term containing a negative shift and a positive shift using Taylor series expansion procedure, and then a three-term scheme is obtained using the theory of finite differences. A fitting factor is introduced in the derived scheme with the help of singular perturbation theory. Thomas algorithm is employed to find the solution to the resulting tridiagonal system of equations. To approve the applicability of the scheme, a few model illustrations have been solved by taking the different values for the perturbation parameter ε, delay parameter δ, and the advanced parameter η. We have presented maximum absolute errors and computational order for the standard examples chosen from the literature.