@inproceedings{bf21c007ac4149c08edfdae63de389a5,

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

abstract = "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.",

keywords = "Collocation of integral relations, Computer algebra system, Krylov subspaces, Multigrid, Preconditioner, Symbolic-numerical algorithm, NAVIER-STOKES EQUATIONS, COMPUTER, COMPUTATION, FLOW",

author = "Shapeev, {Vasily P.} and Vorozhtsov, {Evgenii V.}",

year = "2017",

month = jan,

day = "1",

doi = "10.1007/978-3-319-66320-3_25",

language = "English",

isbn = "9783319663197",

volume = "10490 LNCS",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag GmbH and Co. KG",

pages = "346--361",

editor = "VP Gerdt and W Koepf and WM Seiler and EV Vorozhtsov",

booktitle = "Computer Algebra in Scientific Computing - 19th International Workshop, CASC 2017, Proceedings",

address = "Germany",

note = "19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017 ; Conference date: 18-09-2017 Through 22-09-2017",

}