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Restoration of the merely time-dependent lowest term in a linear Bi-flux diffusion equation
(Springer Heidelberg, 2024) Alosaimi, M.; Tekin, I.; Cetin, M. A.
This paper investigates the inverse problem of determining the merely time-dependent lowest term and the particle concentration in a linear Bi-flux diffusion equation from knowledge of the particle concentration at the left boundary. The unique solvability of this inverse problem is established through the application of the contraction principle for sufficiently small time intervals. To solve this problem computationally, it is reformulated as a nonlinear least-squares minimization problem with simple bounds on the unknown coefficient, and to ensure stability the Tikhonov regularization is employed. The Crank-Nicolson finite-difference scheme is developed to solve the direct problem. On the other hand, the nonlinear least-squares minimization problem is iteratively solved using the built-in subroutine lsqnonlin from the MATLAB optimization toolbox. Numerical findings for two benchmark examples, involving the recovery of smooth and non-smooth time-dependent lowest terms, are presented and analyzed.