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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Volume 16, Number 1, Pages 102–118 (Mi timm531)  
This article is cited in 14 scientific papers (total in 14 papers)

Convergence of the alternating direction method for the numerical solution of a heat conduction equation with delay

A. V. Lekomtsev, V. G. Pimenov

Ural State University
Full-text PDF (492 kB) Citations (14)
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Abstract: Two-dimensional parabolic equations with delay effects in the time component are considered. An alternating direction scheme is constructed for the numerical solution of these equations. The question on the reduction of the problem with inhomogeneous boundary conditions to a problem with homogeneous boundary conditions is considered. The order of approximation error for the alternating direction scheme, stability, and convergence order are investigated.
Keywords: parabolic equations, delay, alternating direction method.
Received: 02.11.2009
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, Volume 272, Issue 1, Pages S101–S118
DOI: https://doi.org/10.1134/S0081543811020088
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: A. V. Lekomtsev, V. G. Pimenov, “Convergence of the alternating direction method for the numerical solution of a heat conduction equation with delay”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 102–118; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S101–S118
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/timm531
  • https://www.mathnet.ru/eng/timm/v16/i1/p102
    • This publication is cited in the following 14 articles:
    1. Dingwen Deng, Jingliang Chen, “Explicit Richardson extrapolation methods and their analyses for solving two-dimensional nonlinear wave equation with delays”, NHM, 18:1 (2023), 412  crossref
    2. Liangcai Mei, Boying Wu, Yingzhen Lin, “Shifted-Legendre orthonormal method for delay heat conduction equation”, Applied Mathematics Letters, 130 (2022), 107996  crossref
    3. M. Ibrahim, V. G. Pimenov, “Crank-Nicolson scheme for two-dimensional in space fractional diffusion equations with functional delay”, Izv. IMI UdGU, 57 (2021), 128–141  mathnet  crossref
    4. Andrei Lekomtsev, Springer Proceedings in Mathematics & Statistics, 333, Differential and Difference Equations with Applications, 2020, 105  crossref
    5. Jing Niu, Lixia Sun, Minqiang Xu, Jinjiao Hou, “A reproducing kernel method for solving heat conduction equations with delay”, Applied Mathematics Letters, 100 (2020), 106036  crossref
    6. 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
    7. Svyatoslav I. Solodushkin, Arsen A. Sagoyan, Irina F. Yumanova, Lecture Notes in Computer Science, 10187, Numerical Analysis and Its Applications, 2017, 617  crossref
    8. Vladimir Pimenov, Ahmed Hendy, Lecture Notes in Computer Science, 10187, Numerical Analysis and Its Applications, 2017, 533  crossref
    9. 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
    10. Svyatoslav I. Solodushkin, Irina F. Yumanova, Rob H. De Staelen, “First order partial differential equations with time delay and retardation of a state variable”, Journal of Computational and Applied Mathematics, 289 (2015), 322  crossref
    11. Andrey Lekomtsev, Vladimir Pimenov, “Convergence of the scheme with weights for the numerical solution of a heat conduction equation with delay for the case of variable coefficient of heat conductivity”, Applied Mathematics and Computation, 256 (2015), 83  crossref
    12. T. E. Romanenko, A. V. Razgulin, “On modeling of distortions suppression in nonlinear optical system with delayed feedback loop”, Math. Models Comput. Simul., 7:3 (2015), 259–270  mathnet  mathnet  crossref  scopus
    13. Vladimir Pimenov, Andrey Lozhnikov, Lecture Notes in Computer Science, 8236, Numerical Analysis and Its Applications, 2013, 437  crossref
    14. V. G. Pimenov, “Chislennye metody resheniya evolyutsionnykh uravnenii s zapazdyvaniem”, Izv. IMI UdGU, 2012, no. 1(39), 103–104  mathnet
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