An Adaptive Method For Time-Fractional Singularly Perturbed Problem

Fractional derivative is widely used in the modeling of fractional differential equations due to its heritability,memorability and spatial anisotropy.the fractional operator has non-locality,which makes the calculation of any non-local differential equation produce dense or even full sparse matrix,resulting in a huge amount of calculation and double storage.The solutions of time fractional singularly perturbed problems often have boundary layers at the boundary,the solutions vary greatly in the boundary layer,which makes numerical solutions difficult.In this paper,the adaptive moving mesh method is studied for boundary layer problems with time fractional singularly perturbed convection-diffusion e-quations.Firstly,the semi-discrete scheme is obtained based on the fast algorith-m₁scheme.Secondly,the fully discrete scheme is obtained by the finite difference method in space.Then,using the new nodes of the current layer,which updates the numerical solution of the previous layer to solve the numerical solution of the new layer.Finally,Several numerical examples are given to verify the effectiveness of the algorithm.