Numerical Solution Methods for a Nonlinear Operator Equation Arising in an Inverse Coefficient Problem

We consider the inverse problem of determining two unknown coefficients in a linear system of partial differential equations using additional information about one of the solution components. The problem is reduced to a nonlinear operator equation for one of the unknown coefficients. The successive...

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Bibliographic Details
Published in:Differential equations Vol. 57; no. 7; pp. 868 - 875
Main Authors: Gavrilov, S. V., Denisov, A. M.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.07.2021
Springer
Subjects:
Difference and Functional Equations
Differential equations
Mathematics
Mathematics and Statistics
Methods
Numerical Methods
Ordinary Differential Equations
Partial Differential Equations
ISSN:0012-2661, 1608-3083
Online Access:Get full text
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Summary:We consider the inverse problem of determining two unknown coefficients in a linear system of partial differential equations using additional information about one of the solution components. The problem is reduced to a nonlinear operator equation for one of the unknown coefficients. The successive approximation method and the Newton method are used to solve this operator equation numerically. Results of calculations illustrating the convergence of numerical methods for solving the inverse problem are presented.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266121070041