Premium
Recovery of timewise‐dependent heat source for hyperbolic PDE from an integral condition
Author(s) -
Huntul M.J.,
Tamsir Mohammad
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6845
Subject(s) - tikhonov regularization , mathematics , inverse problem , discretization , mathematical analysis , regularization (linguistics) , hyperbolic partial differential equation , boundary value problem , nonlinear system , numerical analysis , heat equation , partial differential equation , physics , quantum mechanics , artificial intelligence , computer science
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.