Using a LDG method for solving an inverse source problem of the time-fractional diffusion equation

S Yeganeh, R Mokhtari, S Fouladi
2017 Iranian Journal of Numerical Analysis and Optimization   unpublished
In this paper, we apply a local discontinuous Galerkin (LDG) method to solve some fractional inverse problems. In fact, we determine a time-dependent source term in an inverse problem of the time-fractional diffusion equation. The method is based on a finite difference scheme in time and a LDG method in space. A numerical stability theorem as well as an error estimate is provided. Finally, some numerical examples are tested to confirm theoretical results and to illustrate effectiveness of the
more » ... thod. It must be pointed out that proposed method generates stable and accurate numerical approximations without using any regularization methods which are necessary for other numerical methods for solving such ill-posed inverse problems.