USING A LDG METHOD FOR SOLVING AN INVERSE SOURCE PROBLEM OF THE TIME-FRACTIONAL DIFFUSION EQUATION

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YEGANEH S.; MOKHTARI R.; FOULADI S.

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Paper Information

Journal: IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION Year:2017 | Volume:7 | Issue:2 Page(s): 115-135

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Title

USING A LDG METHOD FOR SOLVING AN INVERSE SOURCE PROBLEM OF THE TIME-FRACTIONAL DIFFUSION EQUATION

Author(s)

YEGANEH S. | MOKHTARI R. | FOULADI S. | Issue Writer Certificate

Keywords

LOCAL DISCONTINUOUS GALERKIN METHODQ1

INVERSE SOURCE PROBLEMQ1

TIME-FRACTIONAL DIFFUSION EQUATIONQ1

Abstract

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.

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APA: Copy

YEGANEH, S., MOKHTARI, R., & FOULADI, S.. (2017). USING A LDG METHOD FOR SOLVING AN INVERSE SOURCE PROBLEM OF THE TIME-FRACTIONAL DIFFUSION EQUATION. IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION, 7(2), 115-135. SID. https://sid.ir/paper/260826/en

Vancouver: Copy

YEGANEH S., MOKHTARI R., FOULADI S.. USING A LDG METHOD FOR SOLVING AN INVERSE SOURCE PROBLEM OF THE TIME-FRACTIONAL DIFFUSION EQUATION. IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION[Internet]. 2017;7(2):115-135. Available from: https://sid.ir/paper/260826/en

IEEE: Copy

S. YEGANEH, R. MOKHTARI, and S. FOULADI, “USING A LDG METHOD FOR SOLVING AN INVERSE SOURCE PROBLEM OF THE TIME-FRACTIONAL DIFFUSION EQUATION,” IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION, vol. 7, no. 2, pp. 115–135, 2017, [Online]. Available: https://sid.ir/paper/260826/en

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