Determination of control parameter in an inverse time fractional‎ ‎diffusion equation using a linearized fourth-order finite difference scheme

Document Type : Research Article

Authors

1 Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran

2 Department of Mathematics‎, ‎Faculty of Mathematics‎, ‎Statistics and Computer, Semnan University‎, ‎Semnan‎, ‎Iran

Abstract

‎The problem of finding the space‎- ‎or time-dependent control parameter in partial differential equations has increasingly appeared in physical‎ ‎phenomena‎, ‎for example‎, ‎in the study of control theory‎, ‎heat conduction process‎, ‎and‎ ‎chemical diffusion‎. ‎This study aims to construct an efficient numerical method to determine a time-dependent source term in a time fractional diffusion‎ ‎equation subject to over-specification at a point in the spatial domain‎. ‎We use a second order scheme to discretize the equation in the time direction‎, ‎then we replace the space derivative with a fourth-order compact finite difference approximation‎. ‎We will construct a linearized difference scheme and prove the solvability, and unconditional stability of the proposed method‎. ‎Due to the usually ill-posed nature of inverse problems‎, ‎we examine the stability of the method with respect to perturbations of the data‎. ‎We show that the proposed method achieves stable and accurate numerical‎ ‎approximations without using any regularization techniques‎. ‎Numerical experiments show satisfactory results for problems with smooth‎, ‎non-smooth‎, ‎and discontinuous initial conditions‎.

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References

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Journal of Mathematical Modeling
Volume 14, Issue 3
August 2026
Pages 1053-1069

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