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May 18, 2026Lobachevskii Journal of Mathematics0 citations

Iterative Identification of the Spacewise Coefficient of the Lowest Derivative in a Parabolic Equation

VVVasilii Vasil’ev AKAnatoly KardashevskyNorth-Eastern Federal University KKKristina KardashevskaiaNorth-Eastern Federal University

Key Points

This research aims to determine the stationary coefficient of the convective term in a parabolic equation using an inverse problem approach.
Used the secant iterative method for numerical solutions.
Applied a finite-difference analogue to the formulated problem.
Evaluated the proposed algorithm on test problems with quasi-solutions.
Demonstrated effective identification of the coefficient using the proposed computation method.
Numerical results showed potential for solving the posed inverse problem.
Achieved reliable outcomes for the test problems.

Abstract

This paper examines an inverse problem of determining the stationary coefficient of the convective term in a parabolic-type equation. As an overdetermination condition, the value of the solution at the final moment of time is specified. To obtain a numerical solution of the finite-difference analogue of the formulated problem, it is proposed to use the secant iterative method. The results of numerical implementation of the proposed computational algorithm are presented for test problems with quasi-solutions.

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