A NAIVE FINITE DIFFERENCE APPROXIMATIONS FOR SINGULARLY PERTURBED PARABOLIC REACTION-DIFFUSION PROBLEMS

Author (s) : B.Mohanapriya, Dr.Senthilmurugan & V.Vimala

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Abstract :
A naïve finite difference approximations for singularlyperturbed parabolic reaction-diffusion problems In this thesis, we treated a Standard Finite Difference Scheme for a singularly perturbed parabolic reaction-diffusion equation. We proved that the Standard Finite Difference Scheme is not a robust technique for solving such problems with singularities. First we discretized the continuous problem in time using the forward Euler method. We proved that the discrete problem satisfied a stability property in the l1 ? norm and l2 ? norm which is not uniform with respect tothe perturbation parameter, as the solution is unbounded when the perturbation parameter goes to zero. Error analysis also showed that the solution of the SFDS is not uniformly convergent in the discrete l1 ? norm with respect to the perturbation parameter, (i.e., the convergence is very poor as the parameter becomes very small). Finally we presented numerical results that confirmed our theoretical findings.

Keywords : naïve finite difference approximations, parabolic reaction-diffusion problems

Conference Date : 30/08/2019

Pages : 343

Paper ID : 19334