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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 2, Pages 237–252 (Mi zvmmf9654)  
This article is cited in 10 scientific papers (total in 10 papers)

Method for constructing solutions of linear ordinary differential equations with constant coefficients

V. V. Karachik

Southern Ural State University, pr. Lenina 76, Chelyabinsk, 454080 Russia
Full-text PDF (297 kB) Citations (10)
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Abstract: For Cauchy problems involving linear differential equations with constant coefficients, a new method for constructing solutions without determining the roots of the characteristic equation is proposed. Formulas for the differentiation of the solution with respect to the equation coefficients are derived, and an approximate analytical solution is found.
Key words: ordinary differential equations with constant coefficients, Cauchy problem, operator series, differentiation with respect to coefficients.
Received: 16.06.2011
Revised: 08.08.2011
English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 2, Pages 219–234
DOI: https://doi.org/10.1134/S0965542512020108
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: V. V. Karachik, “Method for constructing solutions of linear ordinary differential equations with constant coefficients”, Zh. Vychisl. Mat. Mat. Fiz., 52:2 (2012), 237–252; Comput. Math. Math. Phys., 52:2 (2012), 219–234
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf/v52/i2/p237
    • This publication is cited in the following 10 articles:
    1. Dharmendra Kumar Yadav, Sanjay Kumar, Laklalech Nadia, Awadh Bihari Yadav, “Role of multiplicity in examination oriented teaching destroying mathematics quality education”, Journal of Mathematics and Science Teacher, 4:1 (2024), em055  crossref
    2. Elena Rozhkova, Zuxritdin Ergashev, “RECURRENT-OPERATOR METHOD OF SOLUTION SPATIAL DYNAMIC LAME EQUATIONS”, InterConf+, 2022, no. 18(95), 730  crossref
    3. Turmetov B.Kh., Usmanov K.I., Nazarova K.Zh., “On the Operator Method For Solving Linear Integro-Differential Equations With Fractional Conformable Derivatives”, Fractal Fract., 5:3 (2021), 109  crossref  isi
    4. Turmetov B.Kh., “On a Method For Constructing a Solution of Integro-Differential Equations of Fractional Order”, Electron. J. Qual. Theory Differ., 2018, no. 25, 1–14  crossref  mathscinet  isi  scopus
    5. B. Kh. Turmetov, “Normirovannye sistemy i ikh primenenie k postroeniyu reshenii differentsialnykh uravnenii drobnogo poryadka”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 8:1 (2016), 28–33  mathnet  crossref  elib
    6. Ashurov R., Cabada A., Turmetov B., “Operator Method For Construction of Solutions of Linear Fractional Differential Equations With Constant Coefficients”, Fract. Calc. Appl. Anal., 19:1 (2016), 229–252  crossref  mathscinet  zmath  isi  elib  scopus
    7. Meiirkhan B. Borikhanov, Batirkhan Kh. Turmetov, AIP Conference Proceedings, 1759, 2016, 020151  crossref
    8. V. V. Karachik, “Zadachi Koshi i Gursa dlya uravneniya 3-go poryadka”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:2 (2015), 31–43  mathnet  elib
    9. V. V. Karachik, “Construction of polynomial solutions to the Dirichlet problem for the polyharmonic equation in a ball”, Comput. Math. Math. Phys., 54:7 (2014), 1122–1143  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. Valerii V. Karachik, “Polinomialnye resheniya zadachi Dirikhle dlya 3-garmonicheskogo uravneniya v share”, Zhurn. SFU. Ser. Matem. i fiz., 5:4 (2012), 527–546  mathnet
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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