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ON SOME NUMERICAL INTEGRATION CURVES FOR PDE IN NEIGHBORHOOD OF "BUTTERFLY" CATASTROPHE POINT. / Khachay, Oleg Y.; Nosov, Pavel A.
In: Ural Mathematical Journal, Vol. 2, No. 2(3), 2016, p. 127-140.

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

Harvard

Khachay, OY & Nosov, PA 2016, 'ON SOME NUMERICAL INTEGRATION CURVES FOR PDE IN NEIGHBORHOOD OF "BUTTERFLY" CATASTROPHE POINT', Ural Mathematical Journal, vol. 2, no. 2(3), pp. 127-140. https://doi.org/10.15826/umj.2016.2.011

APA

Khachay, O. Y., & Nosov, P. A. (2016). ON SOME NUMERICAL INTEGRATION CURVES FOR PDE IN NEIGHBORHOOD OF "BUTTERFLY" CATASTROPHE POINT. Ural Mathematical Journal, 2(2(3)), 127-140. https://doi.org/10.15826/umj.2016.2.011

Vancouver

Khachay OY, Nosov PA. ON SOME NUMERICAL INTEGRATION CURVES FOR PDE IN NEIGHBORHOOD OF "BUTTERFLY" CATASTROPHE POINT. Ural Mathematical Journal. 2016;2(2(3)):127-140. doi: 10.15826/umj.2016.2.011

Author

Khachay, Oleg Y. ; Nosov, Pavel A. / ON SOME NUMERICAL INTEGRATION CURVES FOR PDE IN NEIGHBORHOOD OF "BUTTERFLY" CATASTROPHE POINT. In: Ural Mathematical Journal. 2016 ; Vol. 2, No. 2(3). pp. 127-140.

BibTeX

@article{796f4153a4144348b4eb51c0e7f0fbaa,
title = "ON SOME NUMERICAL INTEGRATION CURVES FOR PDE IN NEIGHBORHOOD OF {"}BUTTERFLY{"} CATASTROPHE POINT",
abstract = "We consider a three-dimensional nonlinear wave equation with the source term smoothly changing over time and space due to a small parameter. The behavior of solutions of this PDE near the typical “butterfly” catastrophe point is studied. In the framework of matched asymptotic expansions method we derive a nonlinear ODE of the second order depending on three parameters to search for the special solution describing the rapid restructuring of the solution of the PDE in a small neighborhood of the catastrophe point, matching with expansion in a more outer layer. Numerical integration curves of the equation for the leading term of the inner asymptotic expansion are obtained.",
author = "Khachay, {Oleg Y.} and Nosov, {Pavel A.}",
year = "2016",
doi = "10.15826/umj.2016.2.011",
language = "English",
volume = "2",
pages = "127--140",
journal = "Ural Mathematical Journal",
issn = "2414-3952",
publisher = "Институт математики и механики им. Н.Н. Красовского УрО РАН",
number = "2(3)",

}

RIS

TY - JOUR

T1 - ON SOME NUMERICAL INTEGRATION CURVES FOR PDE IN NEIGHBORHOOD OF "BUTTERFLY" CATASTROPHE POINT

AU - Khachay, Oleg Y.

AU - Nosov, Pavel A.

PY - 2016

Y1 - 2016

N2 - We consider a three-dimensional nonlinear wave equation with the source term smoothly changing over time and space due to a small parameter. The behavior of solutions of this PDE near the typical “butterfly” catastrophe point is studied. In the framework of matched asymptotic expansions method we derive a nonlinear ODE of the second order depending on three parameters to search for the special solution describing the rapid restructuring of the solution of the PDE in a small neighborhood of the catastrophe point, matching with expansion in a more outer layer. Numerical integration curves of the equation for the leading term of the inner asymptotic expansion are obtained.

AB - We consider a three-dimensional nonlinear wave equation with the source term smoothly changing over time and space due to a small parameter. The behavior of solutions of this PDE near the typical “butterfly” catastrophe point is studied. In the framework of matched asymptotic expansions method we derive a nonlinear ODE of the second order depending on three parameters to search for the special solution describing the rapid restructuring of the solution of the PDE in a small neighborhood of the catastrophe point, matching with expansion in a more outer layer. Numerical integration curves of the equation for the leading term of the inner asymptotic expansion are obtained.

UR - https://elibrary.ru/item.asp?id=27447892

U2 - 10.15826/umj.2016.2.011

DO - 10.15826/umj.2016.2.011

M3 - Article

VL - 2

SP - 127

EP - 140

JO - Ural Mathematical Journal

JF - Ural Mathematical Journal

SN - 2414-3952

IS - 2(3)

ER -

ID: 7010556