On approximate solution of the Dixon integral equation and some its generalizations
The paper is devoted to the study and numerical analytical solution of Fredholm-type integral equations of the second kind with symmetric kernels represented by homogeneous functions of degree (-1). The well-known Dixon equation and some its direct generalizations are specially considered. The equat...
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| Veröffentlicht in: | Computational mathematics and mathematical physics Jg. 57; H. 7; S. 1158 - 1166 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Moscow
Pleiades Publishing
01.07.2017
Springer Nature B.V |
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| ISSN: | 0965-5425, 1555-6662 |
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| Abstract | The paper is devoted to the study and numerical analytical solution of Fredholm-type integral equations of the second kind with symmetric kernels represented by homogeneous functions of degree (-1). The well-known Dixon equation and some its direct generalizations are specially considered. The equations are solved by passing to a Wiener–Hopf equation and applying the kernel averaging method. Results of numerical calculations are presented. |
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| AbstractList | The paper is devoted to the study and numerical analytical solution of Fredholm-type integral equations of the second kind with symmetric kernels represented by homogeneous functions of degree (-1). The well-known Dixon equation and some its direct generalizations are specially considered. The equations are solved by passing to a Wiener-Hopf equation and applying the kernel averaging method. Results of numerical calculations are presented. |
| Author | Barseghyan, A. G. |
| Author_xml | – sequence: 1 givenname: A. G. surname: Barseghyan fullname: Barseghyan, A. G. email: anibarseghyan@mail.ru organization: Institute of Mathematics, National Academy of Sciences of the Republic of Armenia |
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| Cites_doi | 10.1007/BF01085507 10.1134/S1063772913090011 10.1134/S0965542515050061 |
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| Copyright | Pleiades Publishing, Ltd. 2017 Computational Mathematics and Mathematical Physics is a copyright of Springer, 2017. |
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| DOI | 10.1134/S0965542517070041 |
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| Keywords | Wiener–Hopf equation factorization kernel averaging method Dixon equation |
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| References | Sakhnovich (CR5) 2007 Krein (CR6) 1958; 13 Barsegyan, Ter-Avetisyan (CR12) 2013; 90 Dixon (CR1) 1926; 27 Titchmarsh (CR3) 1948 Ts. Gokhberg, Fel’dman (CR10) 1974 Polozhii, Chalenko (CR11) 1964 Barsegyan, Engibaryan (CR8) 2015; 55 Yakubovich (CR7) 2014 Arabadzhyan, Engibaryan (CR9) 1987; 36 Dixon (CR2) 1923; 22 Morse, Feshbach (CR4) 1953 A. C. Dixon (376_CR2) 1923; 22 A. G. Barsegyan (376_CR12) 2013; 90 I. Ts. Gokhberg (376_CR10) 1974 L. A. Sakhnovich (376_CR5) 2007 E. C. Titchmarsh (376_CR3) 1948 G. N. Polozhii (376_CR11) 1964 P. M. Morse (376_CR4) 1953 L. G. Arabadzhyan (376_CR9) 1987; 36 A. C. Dixon (376_CR1) 1926; 27 A. G. Barsegyan (376_CR8) 2015; 55 M. G. Krein (376_CR6) 1958; 13 S. Yakubovich (376_CR7) 2014 |
| References_xml | – volume: 22 start-page: 201 issue: 2 year: 1923 end-page: 222 ident: CR2 article-title: Some limiting classes in the theory of integral equations publication-title: Proc. London Math. Soc. – volume: 13 start-page: 3 issue: 5 year: 1958 end-page: 120 ident: CR6 article-title: Integral equations on a half-line with a kernel depending on the difference of the arguments publication-title: Usp. Mat. Nauk – year: 1964 ident: CR11 article-title: The strip method for solving integral equations publication-title: Topics in Mathematical Physics and Function Theory – volume: 27 start-page: 233 issue: 2 year: 1926 end-page: 272 ident: CR1 article-title: On the solving nuclei of certain integral equation whose nuclei are homogeneous and of degree–1, and the solution of a class of linear functional equations publication-title: Proc. London Math. Soc. – volume: 36 start-page: 745 year: 1987 end-page: 791 ident: CR9 article-title: Convolution equations and nonlinear functional equations publication-title: J. Sov. Math. doi: 10.1007/BF01085507 – year: 2014 ident: CR7 publication-title: On the generalized Dixon integral equation – year: 1953 ident: CR4 publication-title: Methods of Theoretical Physics – year: 1948 ident: CR3 publication-title: Introduction to the Theory of Fourier Integrals – start-page: 289 year: 2007 end-page: 308 ident: CR5 article-title: On triangular factorization of positive operators publication-title: Operator Theory: Advances and Applications – volume: 90 start-page: 686 issue: 9 year: 2013 end-page: 691 ident: CR12 article-title: Solution of the transfer equation in a moving medium publication-title: Astron. Rep. doi: 10.1134/S1063772913090011 – year: 1974 ident: CR10 publication-title: Convolution Equations and Projection Methods for Their Solutions – volume: 55 start-page: 834 issue: 5 year: 2015 end-page: 843 ident: CR8 article-title: Approximate solution of Wiener–Hopf integral equations and its discrete counterparts publication-title: Comput. Math. Math. Phys. doi: 10.1134/S0965542515050061 – start-page: 289 volume-title: Operator Theory: Advances and Applications year: 2007 ident: 376_CR5 – volume: 55 start-page: 834 issue: 5 year: 2015 ident: 376_CR8 publication-title: Comput. Math. Math. Phys. doi: 10.1134/S0965542515050061 – volume: 27 start-page: 233 issue: 2 year: 1926 ident: 376_CR1 publication-title: Proc. London Math. Soc. – volume-title: Introduction to the Theory of Fourier Integrals year: 1948 ident: 376_CR3 – volume: 36 start-page: 745 year: 1987 ident: 376_CR9 publication-title: J. Sov. Math. doi: 10.1007/BF01085507 – volume-title: Convolution Equations and Projection Methods for Their Solutions year: 1974 ident: 376_CR10 – volume: 13 start-page: 3 issue: 5 year: 1958 ident: 376_CR6 publication-title: Usp. Mat. Nauk – volume-title: On the generalized Dixon integral equation year: 2014 ident: 376_CR7 – volume-title: Methods of Theoretical Physics year: 1953 ident: 376_CR4 – volume: 22 start-page: 201 issue: 2 year: 1923 ident: 376_CR2 publication-title: Proc. London Math. Soc. – volume: 90 start-page: 686 issue: 9 year: 2013 ident: 376_CR12 publication-title: Astron. Rep. doi: 10.1134/S1063772913090011 – volume-title: Topics in Mathematical Physics and Function Theory year: 1964 ident: 376_CR11 |
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| SubjectTerms | Computational Mathematics and Numerical Analysis Fredholm equations Integral equations Kernels Mathematical analysis Mathematics Mathematics and Statistics Wiener Hopf equations |
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| Title | On approximate solution of the Dixon integral equation and some its generalizations |
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