Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69777220171001Using a LDG method for solving an inverse source problem of the time-fractional diffusion equationاستفاده از یک روش LDGبرای حل مساله منبع وارون از نوع معادله انتشار کسری-زمانی1151352459110.22067/ijnao.v7i2.62042ENS.YeganehDepartment of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-
83111, Iran.R.MokhtariDepartment of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-
83111, Iran.0000-0002-1420-0949S.FouladiDepartment of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-
83111, Iran.Journal Article19700101In 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.https://ijnao.um.ac.ir/article_24591_7602ffbeb5b87ec2fc9fdb723942918a.pdf