Solving Time-Fractional Diffusion Equation: A Finite-Element Approach

Abstract

The numerical solution for a time-fractional diffusion equation supplemented with initial and boundary conditions is considered. The scheme is based on the Galerkin finite element method. The uniform space discretization is applied to study the stability of the solution of the problem within our approach. An analytically solvable example is presented to make a comparison between the exact solution and our numerical solution. By presenting the absolute error with different step-sizes and different values for time-fractional derivative, reliability and efficiency of our proposed numerical method is manifested.

Keywords

• Time-Fractional Diffusion Equation
• Finite Element Method