Stable numerical solution of an inverse coefficient problem for a time fractional reaction-diffusion equation‎

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Mathematical sciences, University of Mazandaran, ‎P.O‎. ‎Box‎: ‎47416-95447‎, Babolsar, Iran.

2 Department of Applied Mathematics‎, ‎University of Mazandaran‎, ‎P.O‎. ‎Box‎: ‎47416-95447‎, ‎Babolsar‎, ‎Iran

3 Department of Mathematics‎, ‎Faculty of Mathematics‎, ‎Statistics and Computer Science‎, ‎Semnan University‎, ‎Semnan‎, ‎Iran‎

Abstract

‎In this paper‎, ‎an inverse problem of determining an unknown reaction coefficient in a one-dimensional time-fractional reaction-diffusion equation is considered‎. ‎This inverse problem is generally ill-posed‎. ‎For this reason‎, ‎the mollification regularization technique with the generalized cross-validation criteria will be employed to find an equivalent stable problem‎. ‎Afterward‎, ‎a finite difference marching scheme is introduced to solve this regularized problem‎. ‎The stability and convergence of the numerical solution are investigated‎. ‎In the end‎, ‎some numerical examples are presented to verify the ability and effectiveness of the proposed algorithm‎.

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