PARAMETER UNIFORM NUMERICAL METHOD FOR SINGULARLY PERTURBED DIFFERENTIAL EQUATION WITH A LARGE DELAY

This study attempted to introduce the finite difference method (FDM) for parameteruniform numerical schemes for singularly perturbed differential equations with a large delay that involve one governing equation together with some boundary conditions over a domain. It is known that the classical numerical methods are not satisfactory when applied to solve singularly perturbed problems in delayed differential equations. The proposed scheme is analyzed for convergence. An approximate solution to differential equations that satisfies a given relationship between various of its derivatives in some given region of space along with some boundary conditions and along the edges of this domain, along with the ability to use a mesh of numerical analysis to accurately discretized domains of any size and shape, makes the numerical method a powerful tool for numerical analysis problems in these areas. These include improvements in methodology and shishk in meshes, as well as techniques to improve efficiency and estimate the error bound. Some aspects closely related to the finite difference method have also been investigated. The numerical results are tabulated in terms of maximum absolute errors and it observed that the present method is accurate results show the applicability and efficiency of the proposed scheme. Graphs plotted for the solution with varying shifts show the effect of small shifts on the boundary layer behavior of the solution. The numerical analyses of the method reveal that the method is able to produce uniformly convergent solutions with a quadratic convergence rate.