Several remarks on numerical solution of the one-dimensional coefficient inverse problem
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A. L. Karchevsky
Abstract
- In the work we will introduce some results of numerical experiments, that allowed the author to choose a certain tactic for the numerical solution of onedimensional coefficient inverse problems which are reduced to minimization of the discrepancy functional. Principle distinction from the well-known approach is in the following: we will use the Laplace transform instead of the Fourier transform with respect to the time variable. In the work we will present a new method of derivation of a gradient for the discrepancy functional. The difference of this way is in the following: it is suitable to obtain analytic formulas for the gradient both in the case investigated for one equation and for a system of equations. As was shown in the numerical experiment which results are introduced in the work, represented considerations and recommendations may be useful for numerical solution of the coefficient inverse problem.
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Articles in the same Issue
- Contents
- Regularized data-driven construction of fuzzy controllers
- Stable identification of piecewise-constant potentials from fixed-energy phase shifts
- Several remarks on numerical solution of the one-dimensional coefficient inverse problem
- Reconstruction of the potential from I-function
- Some inverse problems for Schrödinger operator with Kato potential
- Inverse spectral problems for higher-order differential operators with a singularity
Articles in the same Issue
- Contents
- Regularized data-driven construction of fuzzy controllers
- Stable identification of piecewise-constant potentials from fixed-energy phase shifts
- Several remarks on numerical solution of the one-dimensional coefficient inverse problem
- Reconstruction of the potential from I-function
- Some inverse problems for Schrödinger operator with Kato potential
- Inverse spectral problems for higher-order differential operators with a singularity
