Analysis of Nonlocal Problem for Loaded Parabolic Equation via Numerical Method

Saule Kuanysh, Zh. M. Kadirbayeva

2025

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DOI 10.1134/s1995080225612214
Data confidence 70 medium
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Abstract

Abstract This paper investigates a nonlocal problem for a loaded parabolic equation defined on a closed domain. By applying spatial discretization, the original problem is transformed into a two-point boundary value problem for a system of loaded ordinary differential equations. To address this problem, the Dzhumabaev parameterization method is utilized. Based on this approach, a numerical algorithm is developed to solve the original problem. The effectiveness of the proposed method is demonstrated through two computational examples. The obtained numerical results are compared with the exact solutions to validate the accuracy of the algorithm.