Robust Numerical Method For Singularly Perturbed Parabolic Problems With Negative Lag

<strong>Abstract:</strong> In this project a robust numerical method for singularly perturbed parabolic problems with negative lag in the temporal direction is presented.The general objective of this project is to develop and analysis a parameter uniform numerical scheme for singularly perturbed parabolic problems with negative lag. The method comprises the back word Euler method is used for the temporal discretization and the non-standard finite difference method is used for the spatial discretization. The extrapolation technique is done using Richardson-Extrapolation method to improve the order of convergence in the spatial direction. The stability and uniform convergence analysis are demonstrated using the solution bound and the truncation error bound. For scene model examples the maximum absolute error and the rate of convergence for different values of the perturbation parameter (ε), and mesh size are tabulated in tables. From the theoretical and numerical results are observed that the proposed method is ε−uniformly convergent. The reported examples illustrate that the method is efficient and accurate.The numerical results are also described graphically for different values of perturbation parameter (ε), and mesh size. The numerical results are also tabulated in comparison with the previous methods .The comparison indicates that the result of the proposal scheme gives more accurate solutions and a higher rate of convergence as compared to some previous finding available in the literature.