Estimates for Taylor series method to linear total systems of PDEs

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Estimates for Taylor series method to linear total systems of PDEs. / Babadzanjanz, Levon K.; Pototskaya, Irina Yu ; Pupysheva, Yulia Yu.

In: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, Vol. 16, No. 2, 06.2020, p. 112-120.

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Author

Babadzanjanz, Levon K. ; Pototskaya, Irina Yu ; Pupysheva, Yulia Yu. / Estimates for Taylor series method to linear total systems of PDEs. In: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya. 2020 ; Vol. 16, No. 2. pp. 112-120.

BibTeX

@article{11389ae7f7a34664a86470b5e34d5472,

title = "Estimates for Taylor series method to linear total systems of PDEs",

abstract = "A large number of differential equations can be reduced to polynomial form. As was shown in a number of works by various authors, one of the best methods for the numerical solution of the initial value problem for such ODE systems is the method of Taylor series. In this article we consider the Cauchy problem for the total linear PDE system, and then — a theorem about the accuracy of its solutions by this method is formulated and proved. In the final part of the article, four examples of total systems of partial differential equations to the well-known two-body problem are proposed: two of them are related to the Kepler equation, one to the motion of a point in the orbit plane, and the last to the motion of the orbit plane.",

keywords = "Numerical PDE system integration, Polynomial system, Taylor series method, Total linear PDE system",

author = "Babadzanjanz, {Levon K.} and Pototskaya, {Irina Yu} and Pupysheva, {Yulia Yu}",

year = "2020",

month = jun,

doi = "10.21638/11701/SPBU10.2020.203",

language = "English",

volume = "16",

pages = "112--120",

journal = " ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ",

issn = "1811-9905",

publisher = "Издательство Санкт-Петербургского университета",

number = "2",

}

RIS

TY - JOUR

T1 - Estimates for Taylor series method to linear total systems of PDEs

AU - Babadzanjanz, Levon K.

AU - Pototskaya, Irina Yu

AU - Pupysheva, Yulia Yu

PY - 2020/6

Y1 - 2020/6

N2 - A large number of differential equations can be reduced to polynomial form. As was shown in a number of works by various authors, one of the best methods for the numerical solution of the initial value problem for such ODE systems is the method of Taylor series. In this article we consider the Cauchy problem for the total linear PDE system, and then — a theorem about the accuracy of its solutions by this method is formulated and proved. In the final part of the article, four examples of total systems of partial differential equations to the well-known two-body problem are proposed: two of them are related to the Kepler equation, one to the motion of a point in the orbit plane, and the last to the motion of the orbit plane.

AB - A large number of differential equations can be reduced to polynomial form. As was shown in a number of works by various authors, one of the best methods for the numerical solution of the initial value problem for such ODE systems is the method of Taylor series. In this article we consider the Cauchy problem for the total linear PDE system, and then — a theorem about the accuracy of its solutions by this method is formulated and proved. In the final part of the article, four examples of total systems of partial differential equations to the well-known two-body problem are proposed: two of them are related to the Kepler equation, one to the motion of a point in the orbit plane, and the last to the motion of the orbit plane.

KW - Numerical PDE system integration

KW - Polynomial system

KW - Taylor series method

KW - Total linear PDE system

UR - http://www.scopus.com/inward/record.url?scp=85091251220&partnerID=8YFLogxK

U2 - 10.21638/11701/SPBU10.2020.203

DO - 10.21638/11701/SPBU10.2020.203

M3 - Article

AN - SCOPUS:85091251220

VL - 16

SP - 112

EP - 120

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 2

ER -

ID: 72622684