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Trigonometric Hermite interpolation method for Fredholm linear integral equations

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents a new trigonometric composite Hermite interpolation method for solving Fredholm linear integral equations. This operator approximates locally both the function and its derivative, which is known on the subdivision nodes. Then we derive a class of quadrature rules with endpoint corrections based on integrating the composite Hermite interpolant.We also provide error estimation and numerical examples to illustrate that this new operator can provide highly accurate results.
Wydawca
Rocznik
Strony
261--275
Opis fizyczny
Bibliogr. 24 poz., wykr.
Twórcy
  • FST de Settat, Km 3, B.P.: 577 Route de Casablanca, 26000 Settat, Morocco
  • Département de Mathématiques, d’Informatique et des Sciences Physiques, Abdelmalek Essaadi University LaSAD, ENS, 93030, Avenue Moulay Hassan, BP: 209 Martil, Martil 93150, Tetouan, Morocco
Bibliografia
  • [1] M. Ajeddar and A. Lamnii, Smooth reverse subdivision of uniform algebraic hyperbolic B-splines and wavelets, Int. J. Wavelets Multiresolut. Inf. Process. 19 (2021), no. 5, Paper No. 2150018.
  • [2] C. Allouch and P. Sablonnière, Iteration methods for Fredholm integral equations of the second kind based on spline quasi-interpolants, Math. Comput. Simulation 99 (2014), 19-27.
  • [3] C. Allouch, P. Sablonnière and D. Sbibih, Solving Fredholm integral equations by approximating kernels by spline quasi-interpolants, Numer. Algorithms 56 (2011), no. 3, 437-453.
  • [4] C. Allouch, D. Sbibih and M. Tahrichi, Superconvergent Nyström and degenerate kernel methods for Hammerstein integral equations, J. Comput. Appl. Math. 258 (2014), 30-41.
  • [5] C. Allouch, D. Sbibih and M. Tahrichi, Superconvergent product integration method for Hammerstein integral equations, J. Integral Equations Appl. 31 (2019), no. 1, 1-28.
  • [6] K. Atkinson and G. Chandler, The collocation method for solving the radiosity equation for unoccluded surfaces, J. Integral Equations Appl. 10 (1998), no. 3, 253-290.
  • [7] D. Barrera, S. Eddargani, A. Lamnii and M. Oraiche, On nonpolynomial monotonicity-preserving C1 spline interpolation, Comput. Math. Methods 3 (2021), no. 4, Paper No. e1160.
  • [8] D. Barrera, F. Elmokhtari and D. Sbibih, Two methods based on bivariate spline quasi-interpolants for solving Fredholm integral equations, Appl. Numer. Math. 127 (2018), 78-94.
  • [9] A. Bellour, D. Sbibih and A. Zidna, Two cubic spline methods for solving Fredholm integral equations, Appl. Math. Comput. 276 (2016), 1-11.
  • [10] A. H. Borzabadi and O. S. Fard, A numerical scheme for a class of nonlinear Fredholm integral equations of the second kind, J. Comput. Appl. Math. 232 (2009), no. 2, 449-454.
  • [11] C. Conti and R. Morandi, Piecewise C1-shape-preserving Hermite interpolation, Computing 56 (1996), no. 4, 323-341.
  • [12] H. B. Curry and I. J. Schoenberg, On spline distributions and their limits-the polya distribution functions, Amer. Math. Soc. 53 (1947), Paper No. 1114.
  • [13] S. Eddargani, A. Lamnii and M. Lamnii, On algebraic trigonometric integro splines, ZAMM Z. Angew. Math. Mech. 100 (2020), no. 2, Article ID e201900262.
  • [14] S. Eddargani, A. Lamnii, M. Lamnii, D. Sbibih and A. Zidna, Algebraic hyperbolic spline quasi-interpolants and applications, J. Comput. Appl. Math. 347 (2019), 196-209.
  • [15] S. Kumar and I. H. Sloan, A new collocation-type method for Hammerstein integral equations, Math. Comp. 48 (1987), no. 178, 585-593.
  • [16] A. Lahtinen, Shape preserving interpolation by quadratic splines, J. Comput. Appl. Math. 29 (1990), no. 1, 15-24.
  • [17] A. Lamnii, M. Lamnii and F. Oumellal, Computation of Hermite interpolation in terms of B-spline basis using polar forms, Math. Comput. Simulation 134 (2017), 17-27.
  • [18] C. Manni, C1 comonotone Hermite interpolation via parametric cubics, J. Comput. Appl. Math. 69 (1996), no. 1, 143-157.
  • [19] G. Mastroianni, G. V. Milovanović and D. Occorsio, Nyström method for Fredholm integral equations of the second kind in two variables on a triangle, Appl. Math. Comput. 219 (2013), no. 14, 7653-7662.
  • [20] S. Micula and G. Micula, On the superconvergent spline collocation methods for the Fredholm integral equations on surfaces, Math. Balkanica (N. S.) 19 (2005), no. 1-2, 155-166.
  • [21] M. S. Mummy, Hermite interpolation with B-splines, Comput. Aided Geom. Design 6 (1989), no. 2, 177-179.
  • [22] P. Sablonnière, D. Sbibih and M. Tahrichi, High-order quadrature rules based on spline quasi-interpolants and application to integral equations, Appl. Numer. Math. 62 (2012), no. 5, 507-520.
  • [23] I. J. Schoenberg and A. Sharma, Cardinal interpolation and spline functions. V. The B-splines for cardinal Hermite interpolation, Linear Algebra Appl. 7 (1973), 1-42.
  • [24] L. L. Schumaker, On shape preserving quadratic spline interpolation, SIAM J. Numer. Anal. 20 (1983), no. 4, 854-864.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-863b5359-f267-4287-976b-4e56804cb53f
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