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Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 1, Pages 178–189 (Mi timm681)  

This article is cited in 10 scientific papers (total in 10 papers)

Difference schemes for the numerical solution of the heat conduction equation with aftereffect

V. G. Pimenova, A. B. Lozhnikovb

a Ural State University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: A family of grid methods is constructed for the numerical solution of the heat conduction equaiton of a general form with time delay; the methods are based on the idea of separating the current state and the prehistory function. A theorem is obtained on the order of convergence of the methods, which uses the technique of proving similar statements for functional differential equations and methods from the general theory of difference schemes. Results of calculating test examples with constant and variable time delay are presented.

Keywords: numerical methods, heat conduction equation, time delay, difference schemes, interpolation, extrapolation, order of convergence.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 275, suppl. 1, S137–S148

Bibliographic databases:

Document Type: Article
UDC: 519.63
Received: 28.06.2010

Citation: V. G. Pimenov, A. B. Lozhnikov, “Difference schemes for the numerical solution of the heat conduction equation with aftereffect”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 1, 2011, 178–189; Proc. Steklov Inst. Math. (Suppl.), 275, suppl. 1 (2011), S137–S148

Citation in format AMSBIB
\by V.~G.~Pimenov, A.~B.~Lozhnikov
\paper Difference schemes for the numerical solution of the heat conduction equation with aftereffect
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2011
\vol 17
\issue 1
\pages 178--189
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2011
\vol 275
\issue , suppl. 1
\pages S137--S148

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    This publication is cited in the following articles:
    1. Poloskov I.E., “Primenenie skhemy rasshireniya fazovogo prostranstva dlya analiza sistem s raspredelennymi parametrami i zapazdyvaniem”, Vestnik Permskogo universiteta. Seriya: Informatsionnye sistemy i tekhnologii, 2011, no. 12, 63–69  elib
    2. V. G. Pimenov, “Chislennye metody resheniya evolyutsionnykh uravnenii s zapazdyvaniem”, Izv. IMI UdGU, 2012, no. 1(39), 103–104  mathnet
    3. V. G. Pimenov, E. E. Tashirova, “Numerical methods for solving a hereditary equation of hyperbolic type”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 126–136  mathnet  crossref  isi  elib
    4. S. I. Solodushkin, “A difference scheme for the numerical solution of an advection equation with aftereffect”, Russian Math. (Iz. VUZ), 57:10 (2013), 65–70  mathnet  crossref
    5. E. A. Omelchenko, M. V. Plekhanova, P. N. Davydov, “Chislennoe reshenie linearizovannoi kvazistatsionarnoi sistemy uravnenii fazovogo polya s zapazdyvaniem”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 5:2 (2013), 45–51  mathnet
    6. V. G. Pimenov, S. V. Sviridov, “Setochnye metody resheniya uravneniya perenosa s zapazdyvaniem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 3, 59–74  mathnet
    7. E. E. Tashirova, “Skhodimost raznostnogo metoda dlya resheniya dvumernogo volnovogo uravneniya s nasledstvennostyu”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:1 (2015), 78–92  mathnet  elib
    8. V. G. Pimenov, M. A. Panachev, “Odnoshagovye chislennye metody dlya resheniya smeshannykh funktsionalno-differentsialnykh uravnenii”, Tr. IMM UrO RAN, 21, no. 2, 2015, 187–197  mathnet  mathscinet  elib
    9. V. G. Pimenov, A. S. Khendi, “Neyavnyi chislennyi metod resheniya drobnogo uravneniya advektsii-diffuzii s zapazdyvaniem”, Tr. IMM UrO RAN, 22, no. 2, 2016, 218–226  mathnet  crossref  mathscinet  elib
    10. Solodushkin S.I. Yumanova I.F. De Staelen R.H., “A Difference Scheme For Multidimensional Transfer Equations With Time Delay”, J. Comput. Appl. Math., 318:SI (2017), 580–590  crossref  mathscinet  zmath  isi  scopus
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