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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 1, Pages 99–112 (Mi zvmmf10326)  

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

Finite-difference methods for solving loaded parabolic equations

V. M. Abdullayevab, K. R. Aida-zadeba

a Institute of Control Systems, Azerbaijan National Academy of Sciences, Baku, Azerbaijan
b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, ul. B. Vagabzade 9, Baku, AZ1141, Azerbaijan

Abstract: Loaded partial differential equations are solved numerically. For illustrative purposes, a boundary value problem for a parabolic equation with various point loads is considered. By applying difference approximations, the problems are reduced to systems of algebraic equations of special structure, which are solved using a parametric representation involving solutions of auxiliary linear systems with tridiagonal matrices. Numerical results are presented and analyzed.

Key words: loaded differential equation, parabolic equation, grid method, tridiagonal matrix algorithm, system of linear algebraic equations.

DOI: https://doi.org/10.7868/S0044466916010038

Full text: PDF file (192 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:1, 93–105

Bibliographic databases:

UDC: 519.624
Received: 31.03.2014
Revised: 08.04.2015

Citation: V. M. Abdullayev, K. R. Aida-zade, “Finite-difference methods for solving loaded parabolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 56:1 (2016), 99–112; Comput. Math. Math. Phys., 56:1 (2016), 93–105

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. R. Aida-zade, V. M. Abdullayev, “Optimizing placement of the control points at synthesis of the heating process control”, Autom. Remote Control, 78:9 (2017), 1585–1599  mathnet  crossref  isi  elib
    2. Z. Khankishiyev, “On solution of a nonlocal problem with dynamic boundary conditions for a loaded linear parabolic equation by straight-line methods”, Bull. Comput. Appl. Math., 5:1 (2017), 77–98  mathscinet  isi
    3. V. M. Abdullayev, K. R. Aida-zade, “Numerical solution of the problem of determining the number and locations of state observation points in feedback control of a heating process”, Comput. Math. Math. Phys., 58:1 (2018), 78–89  mathnet  crossref  crossref  isi  elib
    4. K. R. Aida-zade, V. A. Hashimov, “Optimization of measurement points positioning in a border control synthesis problem for the process of heating a rod”, Autom. Remote Control, 79:9 (2018), 1643–1660  mathnet  crossref  isi  elib
    5. I. N. Parasidis, E. Providas, “An exact solution method for a class of nonlinear loaded difference equations with multipoint boundary conditions”, J. Differ. Equ. Appl., 24:10 (2018), 1649–1663  crossref  mathscinet  zmath  isi  scopus
    6. I. V. Frolenkov, E. N. Kriger, “O razreshimosti zadachi Koshi dlya odnogo klassa mnogomernykh nagruzhennykh parabolicheskikh uravnenii”, Matematicheskii analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 156, VINITI RAN, M., 2018, 41–57  mathnet  mathscinet
    7. K. R. Aida-zade, V. A. Hashimov, “Feedback control of the plate heating process with optimization of the locations of sources and control”, Autom. Remote Control, 81:4 (2020), 670–685  mathnet  crossref  crossref  isi  elib
    8. V. M. Abdullaev, “Chislennoe reshenie kraevoi zadachi dlya nagruzhennogo parabolicheskogo uravneniya s nelokalnymi granichnymi usloviyami”, Vestnik KRAUNTs. Fiz.-mat. nauki, 32:3 (2020), 15–28  mathnet  crossref
    9. M. Kh. Beshtokov, “Kraevye zadachi dlya nagruzhennogo modifitsirovannogo uravneniya vlagoperenosa drobnogo poryadka s operatorom Besselya i raznostnye metody ikh resheniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:2 (2020), 158–175  mathnet  crossref
    10. A. T. Asanova, A. Zholamankyzy, “O semeistve dvukhtochechnykh kraevykh zadach dlya nagruzhennykh differentsialnykh uravnenii”, Izv. vuzov. Matem., 2021, no. 9, 13–24  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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