Analysis of Nonlocal Problem for Loaded Parabolic Equation via Numerical Method
Kuanysh S.K. Kadirbayeva Z.M.
October 2025Pleiades Publishing
Lobachevskii Journal of Mathematics
2025#46Issue 105417 - 5427 pp.
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.
loaded parabolic equation , non-local condition , numerical solution , parameterization method
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Institute of Mathematics and Mathematical Modeling, Almaty, A26G7T5, Kazakhstan
Al-Farabi Kazakh National University, Almaty, A15E3A7, Kazakhstan
Gumarbek Daykeyev Energo University, Almaty, A15X3C5, Kazakhstan
Kazakh National Women’s Teacher Training University, Almaty, A05M0T6, Kazakhstan
International Information Technology University, Almaty, A15M0F0, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University
Gumarbek Daykeyev Energo University
Kazakh National Women’s Teacher Training University
International Information Technology University
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