A Finite Difference Method on Quasi-uniform Mesh for Time-Fractional Advection-Diffusion Equations with Source Term
Provides a more accurate numerical method for solving time-fractional advection-diffusion equations, which are important in modeling anomalous diffusion processes.
The paper develops an unconditionally stable implicit finite difference method on quasi-uniform meshes for time-fractional advection-diffusion equations with source terms, improving numerical accuracy over uniform grids. Error estimates and numerical experiments confirm the method's effectiveness.
The present paper deals with the numerical solution of time-fractional advection-diffusion equations involving the Caputo derivative with source term by means of an unconditionally stable implicit finite difference method on quasi-uniform grids. We use a special quasi-uniform mesh in order to improve the numerical accuracy of the classical discrete fractional formula for the Caputo derivative. The stability and the convergence of the method are discussed. The error estimates established for a quasi-uniform grid and a uniform one are reported to support the theoretical results. Numerical experiments are carried out to demonstrate the effectiveness of the method.