Numerical solution of source identification multi-point problem of parabolic partial differential equation with Neumann type boundary condition

Authors

  • C. Ashyralyyev Bahcesehir University, Istanbul, Turkey; Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkestan, Kazakhstan; National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan https://orcid.org/0000-0002-6976-2084
  • T.A. Ashyralyyeva Yagshygeldi Kakayev International University of Oil and Gas, Ashgabat, Turkmenistan https://orcid.org/0009-0007-6341-9334

DOI:

https://doi.org/10.31489/2024m3/66-76

Keywords:

inverse problem, source identification, parabolic equation, difference scheme, stability, nonlocal condition, boundary value problem, well-posedness, stability estimates, mixed problem

Abstract

We study a source identification boundary value problem for a parabolic partial differential equation with multi-point Neumann type boundary condition. Stability estimates for the solution of the overdetermined mixed BVP for multi-dimensional parabolic equation were established. The first and second order of accuracy difference schemes for the approximate solution of this problem were proposed. Stability estimates for both difference schemes were obtained. The result of numerical illustration in test example was given.

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Published

2024-09-30

Issue

2024 (115) 3

Section

MATHEMATICS