An initial value technique for singularly perturbed reaction-diffusion problems with a negative shift

V. Subburayan, N. Ramanujam

In this paper, a numerical method named as Initial Value Technique (IVT) is suggested to solve singularly perturbed boundary value problems for second order ordinary differential equations of reaction-diffusion type with a delay (negative shift). In this technique, the original problem of solving the second order differential equation is reduced to solving four first order singularly perturbed differential equations without delay and one algebraic equation with a delay. The singularly perturbed problems are solved by a second order hybrid finite difference scheme. An error estimate is derived by using supremum norm and it is of order $O(\varepsilon+N^{-2}\ln^2 N)$, where $N$ is a discretization parameter and $\varepsilon$ is the perturbation parameter. Numerical results are provided to illustrate the theoretical results.