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Analysis of the errorof differencesolutions as a basisfor improvingaccuracy : научноеиздание Shaydurov Vladimir V.Gileva Lidiya V.Golubev Roman A.2025 год

Analysis of the error of difference solutions as a basis for improving accuracy : научное издание
статья из журнала

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База данных: Каталог библиотеки СФУ
Библиографическое описание: Analysis of the error of difference solutions as a basis for improving accuracy : научное издание / Vladimir V. Shaydurov, Lidiya V. Gileva, Roman A. Golubev. - Текст : непосредственный // Russian Journal of Numerical Analysis and Mathematical Modelling. - 2025. - Т. 40, № 3. - P. 199-207. - ISSN 0927-6467. - ISSN 1569-3988, DOI 10.1515/rnam-2025-0016.
Аннотация: <jats:title>Abstract</jats:title> <jats:p>First, we give a short history of four algorithmic approaches in computational mathematics based on the analysis and use of the asymptotic behavior of the error of an approximate solution where the mesh size of a difference grid tends to zero. These approaches are Richardson’s ‘extrapolation to the limit’, Runge’s accuracy rule, Romberg’s rule for calculating integrals, and improving the grid solutions by high-order differences. The first two approaches were initially developed based on the intuitive conclusion about the asymptotic behavior of the error back in the early 20th century. The last two algorithms, at the time of their appearance in the second half of the 20th century, already used theoretical results on the special asymptotic behavior of the error of quadrature rules or difference solutions.</jats:p> <jats:p>The latter approach, despite its good computational efficiency for ordinary differential equations, has not yet been properly developed for solving multidimensional difference problems. Therefore, as an introductory illustration, we present a method for increasing the order of convergence in time for the solution of an initial boundary value problem for a parabolic equation by correcting the right-hand side with differences of a higher order. The increase in accuracy order is justified theoretically and demonstrated by a numerical example.</jats:p>
Год издания: 2025
Авторы: Shaydurov Vladimir V. , Gileva Lidiya V. , Golubev Roman A.
Издательство: Walter de Gruyter GmbH & Co. KG, Москва
Источник: Russian Journal of Numerical Analysis and Mathematical Modelling
Выпуск: Т. 40, № 3
Номера страниц: 199-207
Держатель оригинала документа: Institute of Computational Modeling, Siberian Branch of Russian Academy of Sciences, Krasnoyarsk, Russia
Количество экземпляров:
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