On the method of expansion on a variable interval for non-stationary problems in continuum mechanics

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On the method of expansion on a variable interval for non-stationary problems in continuum mechanics. / Indeitsev, Dmitry A.; Semenov, Boris N.; Vavilov, Dmitry S.

In: Acta Mechanica, Vol. 232, No. 5, 05.2021, p. 1961-1969.

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

BibTeX

@article{a3fb5cf6d1c74a7c90088c52b2d3d4d6,

title = "On the method of expansion on a variable interval for non-stationary problems in continuum mechanics",

abstract = "The present paper is devoted to the development of the method for searching an approximate solution of non-stationary problems on a variable interval. This method was first proposed by L.I. Slepyan. Here, the field of its applicability has been expanded to systems of equations, including equations of both hyperbolic and parabolic type. We describe the procedure of such approach in detail on a number of classical partial differential equations and compare the obtained results with exact analytical solution. Also, we consider a dynamic non-coupled thermoelastic problem. The method of expansion on a variable interval allows us to estimate the material response to a thermal disturbance at a large distance from the source.",

author = "Indeitsev, {Dmitry A.} and Semenov, {Boris N.} and Vavilov, {Dmitry S.}",

year = "2021",

month = may,

doi = "10.1007/s00707-020-02890-6",

language = "English",

volume = "232",

pages = "1961--1969",

journal = "Acta Mechanica",

issn = "0001-5970",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - On the method of expansion on a variable interval for non-stationary problems in continuum mechanics

AU - Indeitsev, Dmitry A.

AU - Semenov, Boris N.

AU - Vavilov, Dmitry S.

PY - 2021/5

Y1 - 2021/5

N2 - The present paper is devoted to the development of the method for searching an approximate solution of non-stationary problems on a variable interval. This method was first proposed by L.I. Slepyan. Here, the field of its applicability has been expanded to systems of equations, including equations of both hyperbolic and parabolic type. We describe the procedure of such approach in detail on a number of classical partial differential equations and compare the obtained results with exact analytical solution. Also, we consider a dynamic non-coupled thermoelastic problem. The method of expansion on a variable interval allows us to estimate the material response to a thermal disturbance at a large distance from the source.

AB - The present paper is devoted to the development of the method for searching an approximate solution of non-stationary problems on a variable interval. This method was first proposed by L.I. Slepyan. Here, the field of its applicability has been expanded to systems of equations, including equations of both hyperbolic and parabolic type. We describe the procedure of such approach in detail on a number of classical partial differential equations and compare the obtained results with exact analytical solution. Also, we consider a dynamic non-coupled thermoelastic problem. The method of expansion on a variable interval allows us to estimate the material response to a thermal disturbance at a large distance from the source.

UR - http://www.scopus.com/inward/record.url?scp=85098659946&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/0851b7da-26f7-354d-b2ce-520f0157ac93/

U2 - 10.1007/s00707-020-02890-6

DO - 10.1007/s00707-020-02890-6

M3 - Article

AN - SCOPUS:85098659946

VL - 232

SP - 1961

EP - 1969

JO - Acta Mechanica

JF - Acta Mechanica

SN - 0001-5970

IS - 5

ER -

ID: 73686637