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

Автор(ы)
Zhenhai Liu
Saule Kuanysh
Дата публикации
1 января 2025 г.
Тип
journal article
Издатель
American Institute of Mathematical Sciences
Журнал
Том
10
Выпуск
12
Первая страница
29454
Последняя страница
29469
DOI
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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W4417345731.pdf

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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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