| Abstract: |
| We propose a uniformly convergent finite difference scheme to solve singularly perturbed time-dependent reaction-diffusion and convection-diffusion problems in the framework of method of lines. Our approach consists of using the fitted operator finite difference method to discretize the spatial derivatives followed by a time discretization. Richardson extrapolation is performed in space to improve the accuracy of the method. We prove that the method is uniformly convergent with respect to the perturbation and the discretization parameters. We present numerical simulations to illustrate and confirm the theoretical results. |
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