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The inverse problem of the simultaneous determination of the right-hand side and the lowest coefficients in parabolic equations. (English) Zbl 1368.65175
Dimov, Ivan (ed.) et al., Numerical analysis and its applications. 6th international conference, NAA 2016, Lozenetz, Bulgaria, June 15–22, 2016. Revised selected papers. Cham: Springer (ISBN 978-3-319-57098-3/pbk; 978-3-319-57099-0/ebook). Lecture Notes in Computer Science 10187, 633-639 (2017).
Summary: In this paper, we propose a numerical scheme to solve the inverse problem of determining two lower coefficients that depends on time only in the parabolic equation. The time dependence of the right-hand side of a parabolic equation is determined using additional solution values at points of the computational domain. For solving the nonlinear inverse problem, linearized approximations in time are constructed using the fully implicit scheme, and standard finite difference procedures are used in space. The results of numerical experiments are presented, confirming the capabilities of the proposed computational algorithms for solving the coefficients inverse problem.
For the entire collection see [Zbl 1360.65014].
MSC:
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35R30 Inverse problems for PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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