L1-Finite Difference Method for Inverse Source Problem of Fractional Diffusion Equation

Abstract

The numerical solution of inverse source problem for time fractional diffusion equation was studied: the time fractional derivative was is discretized by L1 algorithm, and the space derivative was approximated by central difference. The L1-finite difference scheme of the inverse source problem was constructed with the accuracy of O(τ 2–α + h 2). By adding a random disturbance to the final value and combining with the discrete scheme of L1-finite difference method, the algorithm flow was given. The effectiveness of L1-finite difference method for solve the inverse problem of time fractional diffusion equation is verified by numerical examples. The method provides an effective reference scheme for the numerical solution of the inverse problem.