Legendre–Kantorovich method for Fredholm integral equations of the second kind

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dc.citation.epage482
dc.citation.issue3
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage471
dc.contributor.affiliationУніверситет Мохаммеда І
dc.contributor.affiliationUniversity Mohammed I
dc.contributor.authorАллуч, К.
dc.contributor.authorАрраі, М.
dc.contributor.authorБоуда, Х.
dc.contributor.authorТахрічі, М.
dc.contributor.authorArrai, M.
dc.contributor.authorAllouch, C.
dc.contributor.authorBouda, H.
dc.contributor.authorTahrichi, M.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T11:32:56Z
dc.date.created2022-02-28
dc.date.issued2022-02-28
dc.description.abstractУ цій роботі розглядається поліноміальний метод Канторовича для чисельного розв’язування інтегрального рівняння Фредгольма другого роду з гладким ядром. Використовувана проекція є або ортогональною проекцією, або інтерполяційною проекцією з використанням базису поліномів Лежандра. Встановлено порядок збіжності запропонованого методу та порядок суперзбіжності ітераційних версій. Показано, що ці порядки збіжності справедливі у відповідних дискретних методах, які отримані заміною інтеграла квадратурою. Для ілюстрації теоретичних оцінок наведено числові приклади.
dc.description.abstractIn the present paper, we consider polynomially based Kantorovich method for the numerical solution of Fredholm integral equation of the second kind with a smooth kernel. The used projection is either the orthogonal projection or an interpolatory projection using Legendre polynomial bases. The order of convergence of the proposed method and those of superconvergence of the iterated versions are established. We show that these orders of convergence are valid in the corresponding discrete methods obtained by replacing the integration by a quadrature rule. Numerical examples are given to illustrate the theoretical estimates.
dc.format.extent471-482
dc.format.pages12
dc.identifier.citationLegendre–Kantorovich method for Fredholm integral equations of the second kind / M. Arrai, C. Allouch, H. Bouda, M. Tahrichi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 471–482.
dc.identifier.citationenLegendre–Kantorovich method for Fredholm integral equations of the second kind / M. Arrai, C. Allouch, H. Bouda, M. Tahrichi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 471–482.
dc.identifier.doi10.23939/mmc2022.03.471
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63456
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 3 (9), 2022
dc.relation.ispartofMathematical Modeling and Computing, 3 (9), 2022
dc.relation.references[1] Atkinson K. E. The Numerical Solution of Integral Equations of the Second Kind. Cambridge University Press, Cambridge (1997).
dc.relation.references[2] Atkinson K. E., Han W. Theoretical numerical analysis. Springer Verlag, Berlin (2005).
dc.relation.references[3] Kantorovich L., Krylov V. Approximate Methods of Higher Analysis. Noordhoff, Groningen, The Netherlands (1964).
dc.relation.references[4] Golberg M. Discrete Polynomial-Based Galerkin Methods for Fredholm Integral Equations. Journal of Integral Equations and Applications. 6 (2), 197–211 (1994).
dc.relation.references[5] Kulkarni R. P., Nelakanti G. Iterated discrete polynomially based Galerkin methods. Applied Mathematics and Computation. 146 (1), 153–165 (2003).
dc.relation.references[6] Nelakanti G., Panigrahi B. L. Legendre Galerkin method for weakly singular Fredholm integral equations and the corresponding eigenvalue problem. Journal of Applied Mathematics and Computing. 43, 175–197 (2013).
dc.relation.references[7] Long G., Nelakanti G., Sahani M. M. Polynomially based multi-projection methods for Fredholm integral equations of the second kind. Applied Mathematics and Computation. 215 (1), 147–155 (2009).
dc.relation.references[8] Das P., Nelakanti G. Convergence analysis of discrete Legendre spectral projection methods for Hammerstein integral equations of mixed type. Applied Mathematics and Computation. 265, 574–601 (2015).
dc.relation.references[9] Das P., Nelakanti G. Error analysis of discrete legendre multi-projection methods for nonlinear Fredholm integral equations. Numerical Functional Analysis and Optimization. 38 (5), 549–574 (2017).
dc.relation.references[10] Das P., Long G., Nelakanti G. Discrete Legendre spectral projection methods for Fredholm–Hammerstein integral equations. Journal of Computational and Applied Mathematics. 278, 293–305 (2015).
dc.relation.references[11] Chen C., Golberg M. Discrete projection methods for integral equations. Computational Mechanics Publications (1997).
dc.relation.references[12] Sloan I. H. Four variants of the Gaterkin method for Integral equations of the second kind. IMA Journal of Numerical Analysis. 4 (1), 9–17 (1984).
dc.relation.references[13] Golberg M. Improved convergence rates for some discrete Galerkin methods. Journal of Integral Equations and Applications. 8 (3), 307–335 (1996).
dc.relation.references[14] Sloan I. H. Polynomial interpolation and hyperinterpolation over general regions. Journal of Approximation Theory. 83 (2), 238–254 (1995).
dc.relation.referencesen[1] Atkinson K. E. The Numerical Solution of Integral Equations of the Second Kind. Cambridge University Press, Cambridge (1997).
dc.relation.referencesen[2] Atkinson K. E., Han W. Theoretical numerical analysis. Springer Verlag, Berlin (2005).
dc.relation.referencesen[3] Kantorovich L., Krylov V. Approximate Methods of Higher Analysis. Noordhoff, Groningen, The Netherlands (1964).
dc.relation.referencesen[4] Golberg M. Discrete Polynomial-Based Galerkin Methods for Fredholm Integral Equations. Journal of Integral Equations and Applications. 6 (2), 197–211 (1994).
dc.relation.referencesen[5] Kulkarni R. P., Nelakanti G. Iterated discrete polynomially based Galerkin methods. Applied Mathematics and Computation. 146 (1), 153–165 (2003).
dc.relation.referencesen[6] Nelakanti G., Panigrahi B. L. Legendre Galerkin method for weakly singular Fredholm integral equations and the corresponding eigenvalue problem. Journal of Applied Mathematics and Computing. 43, 175–197 (2013).
dc.relation.referencesen[7] Long G., Nelakanti G., Sahani M. M. Polynomially based multi-projection methods for Fredholm integral equations of the second kind. Applied Mathematics and Computation. 215 (1), 147–155 (2009).
dc.relation.referencesen[8] Das P., Nelakanti G. Convergence analysis of discrete Legendre spectral projection methods for Hammerstein integral equations of mixed type. Applied Mathematics and Computation. 265, 574–601 (2015).
dc.relation.referencesen[9] Das P., Nelakanti G. Error analysis of discrete legendre multi-projection methods for nonlinear Fredholm integral equations. Numerical Functional Analysis and Optimization. 38 (5), 549–574 (2017).
dc.relation.referencesen[10] Das P., Long G., Nelakanti G. Discrete Legendre spectral projection methods for Fredholm–Hammerstein integral equations. Journal of Computational and Applied Mathematics. 278, 293–305 (2015).
dc.relation.referencesen[11] Chen C., Golberg M. Discrete projection methods for integral equations. Computational Mechanics Publications (1997).
dc.relation.referencesen[12] Sloan I. H. Four variants of the Gaterkin method for Integral equations of the second kind. IMA Journal of Numerical Analysis. 4 (1), 9–17 (1984).
dc.relation.referencesen[13] Golberg M. Improved convergence rates for some discrete Galerkin methods. Journal of Integral Equations and Applications. 8 (3), 307–335 (1996).
dc.relation.referencesen[14] Sloan I. H. Polynomial interpolation and hyperinterpolation over general regions. Journal of Approximation Theory. 83 (2), 238–254 (1995).
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.subjectінтегральне рівняння Фредгольма
dc.subjectоператор проектування
dc.subjectполіном Лежандра
dc.subjectсуперзбіжність
dc.subjectквадратурне правило
dc.subjectдискретний метод
dc.subjectFredholm integral equation
dc.subjectprojection operator
dc.subjectLegendre polynomial
dc.subjectsuperconvergence
dc.subjectquadrature rule
dc.subjectdiscrete method
dc.titleLegendre–Kantorovich method for Fredholm integral equations of the second kind
dc.title.alternativeМетод Лежандра–Канторовича для інтегральних рівнянь Фредгольма другого роду
dc.typeArticle

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Mathematical Modeling And Computing. – 2022. – Vol. 9, No. 3