Convergence, stability, and error analysis of the method of lines for solving loaded parabolic equations

A. T. Assanova; Zhenhai Liu; Saule Kuanysh; Zh. М. Каdirbayeva

doi:10.3934/math.20251293

Convergence, stability, and error analysis of the method of lines for solving loaded parabolic equations

Автор(ы)

A. T. Assanova

Zhenhai Liu

Saule Kuanysh

Zh. М. Каdirbayeva

Дата публикации

1 января 2025 г.

Тип

journal article

Издатель

American Institute of Mathematical Sciences

Журнал

AIMS Mathematics

Том

10

Выпуск

12

Первая страница

29454

Последняя страница

29469

DOI

10.3934/math.20251293

ISSN

2473-6988

Аннотация

This paper studies the method of lines for solving loaded parabolic equations and provides a theoretical analysis of its convergence, stability, and error estimates. The spatial discretization reduces the original equation to a system of loaded ordinary differential equations solved by the Dzhumabaev parameterization method. Sufficient conditions for the existence and uniqueness of the solution are established, and it is proved that the method achieves second-order accuracy in space and stable convergence. A numerical example confirms the efficiency and reliability of the proposed approach.

Темы

method of lines

convergence analysis

stability analysis

error estimates

existence and uniquen...

second-order accuracy...

spatial discretizatio...

Области науки (FoS)

Mathematics

Applied Mathematics

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Полный текст в открытом доступе, лицензия cc-by-nc-sa; источник: http://www.aimspress.com/aimspress-data/math/2025/12/PDF/math-10-12-1293.pdf

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