The Method of Collocations and Least Residuals Combining the Integral Form of Collocation Equations and the Matching Differential Relations at the Solution of PDEs

Vasily P. Shapeev, Evgenii V. Vorozhtsov

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

2 Цитирования (Scopus)

Аннотация

To increase the accuracy of computations by the method of collocations and least residuals (CLR) it is proposed to increase the number of degrees of freedom with the aid of the following two techniques: an increase in the number of basis vectors and the integration of the linearized partial differential equations (PDEs) over the subcells of each cell of a spatial computational grid. The implementation of these modifications, however, leads to the necessity of increasing the amount of symbolic computations needed for obtaining the work formulas of the new versions of the CLR method. The computer algebra system (CAS) Mathematica has proved to be successful at the execution of all these computations. It is shown that the proposed new symbolic-numeric versions of the CLR method possess a higher accuracy than the previous versions of this method. Furthermore, the version of the CLR method, which employs the integral form of collocation equations, needs a much lesser number of iterations for its convergence than the “differential” CLR method.

Язык оригиналаанглийский
Название основной публикацииComputer Algebra in Scientific Computing - 19th International Workshop, CASC 2017, Proceedings
РедакторыVP Gerdt, W Koepf, WM Seiler, EV Vorozhtsov
ИздательSpringer-Verlag GmbH and Co. KG
Страницы346-361
Число страниц16
Том10490 LNCS
ISBN (печатное издание)9783319663197
DOI
СостояниеОпубликовано - 1 янв 2017
Событие19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017 - Beijing, Китай
Продолжительность: 18 сен 201722 сен 2017

Серия публикаций

НазваниеLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Том10490 LNCS
ISSN (печатное издание)0302-9743
ISSN (электронное издание)1611-3349

Конференция

Конференция19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017
СтранаКитай
ГородBeijing
Период18.09.201722.09.2017

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  • Цитировать

    Shapeev, V. P., & Vorozhtsov, E. V. (2017). The Method of Collocations and Least Residuals Combining the Integral Form of Collocation Equations and the Matching Differential Relations at the Solution of PDEs. В VP. Gerdt, W. Koepf, WM. Seiler, & EV. Vorozhtsov (Ред.), Computer Algebra in Scientific Computing - 19th International Workshop, CASC 2017, Proceedings (Том 10490 LNCS, стр. 346-361). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Том 10490 LNCS). Springer-Verlag GmbH and Co. KG. https://doi.org/10.1007/978-3-319-66320-3_25