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

Iranian Journal of Numerical Analysis and Optimization

مقاله 5، دوره 7، شماره 2 - شماره پیاپی 12، دی 2017، صفحه 115-135   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v7i2.62042

نویسندگان

S. Yeganeh؛ R. Mokhtari^* ؛ S. Fouladi

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156- 83111, Iran.

چکیده

In this paper, we apply a local discontinuous Galerkin (LDG) method to solve some fractional inverse problems. In fact, we determine a timedependent 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 method. 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.

کلیدواژه‌ها

Local discontinuous Galerkin method؛ Inverse source problem؛ Time-fractional diffusion equation

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