On Some Problems of the Numerical Implementation of Nonlinear Systems on Example of KPI Equation

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On Some Problems of the Numerical Implementation of Nonlinear Systems on Example of KPI Equation. / Bogdanov, Alexander V.; Mareev, Vladimir V.

In: EPJ Web of Conferences, Vol. 226, 2020.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{5639a703f42e4e0985de0b3b7b387263,

title = "On Some Problems of the Numerical Implementation of Nonlinear Systems on Example of KPI Equation",

abstract = "Analytical and numerical peculiarities of solving nonlinear problems are con-sidered on examples of wave equations like KdVB and Kadomtsev-Petviashvili-I equa-tion (KPI). KPI is represented in integro-differential form. Main attention is paid to theproblem of asymptotical behavior of solution and appearance of nonphysical artefacts.The numerical solution is carried out by the finite difference method. For a correct rep-resentation of the boundary condition along theyaxis in numerical simulation a methodis proposed for introducing small artificial convection into the original equation in theindicated direction. Along with the introduction of artificial convection, the procedure oftrimming of the integral on the bands adjacent to the upper and lower boundaries of thecalculated region is used. The results obtained by numerical testing, showed sufficientaccuracy and validity of this procedure.",

author = "Bogdanov, {Alexander V.} and Mareev, {Vladimir V.}",

year = "2020",

doi = "202022601003",

language = "English",

volume = "226",

journal = "EPJ Web of Conferences",

issn = "2100-014X",

publisher = "EDP Sciences",

}

RIS

TY - JOUR

T1 - On Some Problems of the Numerical Implementation of Nonlinear Systems on Example of KPI Equation

AU - Bogdanov, Alexander V.

AU - Mareev, Vladimir V.

PY - 2020

Y1 - 2020

N2 - Analytical and numerical peculiarities of solving nonlinear problems are con-sidered on examples of wave equations like KdVB and Kadomtsev-Petviashvili-I equa-tion (KPI). KPI is represented in integro-differential form. Main attention is paid to theproblem of asymptotical behavior of solution and appearance of nonphysical artefacts.The numerical solution is carried out by the finite difference method. For a correct rep-resentation of the boundary condition along theyaxis in numerical simulation a methodis proposed for introducing small artificial convection into the original equation in theindicated direction. Along with the introduction of artificial convection, the procedure oftrimming of the integral on the bands adjacent to the upper and lower boundaries of thecalculated region is used. The results obtained by numerical testing, showed sufficientaccuracy and validity of this procedure.

AB - Analytical and numerical peculiarities of solving nonlinear problems are con-sidered on examples of wave equations like KdVB and Kadomtsev-Petviashvili-I equa-tion (KPI). KPI is represented in integro-differential form. Main attention is paid to theproblem of asymptotical behavior of solution and appearance of nonphysical artefacts.The numerical solution is carried out by the finite difference method. For a correct rep-resentation of the boundary condition along theyaxis in numerical simulation a methodis proposed for introducing small artificial convection into the original equation in theindicated direction. Along with the introduction of artificial convection, the procedure oftrimming of the integral on the bands adjacent to the upper and lower boundaries of thecalculated region is used. The results obtained by numerical testing, showed sufficientaccuracy and validity of this procedure.

UR - https://www.mendeley.com/catalogue/969e01bd-53b6-3d90-ad12-bb0789ce1cf5/

U2 - 202022601003

DO - 202022601003

M3 - Article

VL - 226

JO - EPJ Web of Conferences

JF - EPJ Web of Conferences

SN - 2100-014X

ER -

ID: 51779508