Fitted Mesh Finite Difference Method for Singularly Perturbed Time-Fractional convection diffusion Problem

Abstract

In this thesis, fitted mesh finite difference method is presented for time-fractional parabolic convectiondiffusion problem with variable coefficients. The time-fractional derivative is considered in the Caputo sense. Implicit Euler method is applied to disctretize the temporal variable on a uniformly and then a finite difference method is applied on a piecewise uniform mesh or on Shishkin mesh discretization along the spatial variable. The parameter uniform convergence of the method is proved rigorously. Finally, to validate the proposed scheme, a numerical experimentation is executed and the result of the experiment is in agreement with the theoretical expectation