TY - JOUR
ID - 24591
TI - Using a LDG method for solving an inverse source problem of the time-fractional diffusion equation
JO - Iranian Journal of Numerical Analysis and Optimization
JA - IJNAO
LA - en
SN - 2423-6977
AU - Yeganeh, S.
AU - Mokhtari, R.
AU - Fouladi, S.
AD - Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-
83111, Iran.
Y1 - 2017
PY - 2017
VL - 7
IS - 2
SP - 115
EP - 135
KW - Local discontinuous Galerkin method
KW - Inverse source problem
KW - Time-fractional diffusion equation
DO - 10.22067/ijnao.v7i2.62042
N2 - 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.
UR - https://ijnao.um.ac.ir/article_24591.html
L1 - https://ijnao.um.ac.ir/article_24591_7602ffbeb5b87ec2fc9fdb723942918a.pdf
ER -