Recovery of timewise‐dependent heat source for hyperbolic PDE from an integral condition. (28th August 2020)

• Record Type: Journal Article
• Authors: Huntul, M.J.; Tamsir, Mohammad
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 2(2021)
• Page Start: 1470
• Page End: 1483
• Publication Date: 2020-08-28
• Subjects: hyperbolic equation -- integral condition -- inverse identification problem -- Neumann boundary conditions -- nonlinear optimization -- Tikhonov regularization; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6845
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The inverse problem of recovering the timewise‐dependent heat source coefficient along with the temperature in a second‐order hyperbolic equation with mixed derivative and with initial and Neumann boundary conditions and integral measurement is, for the first time, numerically investigated. The inverse problem considered in this paper has a unique solution. However, it is an ill‐posed problem by being sensitive to noise. The one‐dimensional inverse problem is discretized using the FDM and recast as a nonlinear least‐squares minimization of Tikhonov regularization function. Numerically, this is effectively solved using the MATLAB subroutine lsqnonlin . The present numerical results demonstrate that accurate and stable approximate solutions have been attained.