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Yıl 2020, , 974 - 983, 02.06.2020

Behrouz Parsa Moghaddam , J. A. Tenreiro Machado Parisa Sattari Shajari Zeynab Salamat Mostaghim

https://doi.org/10.15672/hujms.474938
Cited By: 3

Öz

Kaynakça

  • [1] M.A. Abdou and A.A. Nasr, On the numerical treatment of the singular integral equation of the second kind, Appl. Math. Comput. 143 (2-3), 373–380, 2003.
  • [2] K. Al-Khaled and M. Alquran, Convergence and norm estimates of Hermite interpo- lation at zeros of Chevyshev polynomials, SpringerPlus, 5 (1), 2016.
  • [3] A.A. Badr, Integro-differential equation with Cauchy kernel, J. Comput. Appl. Math. 134 (1-2), 191–199, 2001.
  • [4] P. Baratella and A.P. Orsi, A new approach to the numerical solution of weakly singular Volterra integral equations, J. Comput. Appl. Math. 163 (2), 401–418, 2004.
  • [5] S. Bhattacharya and B.N. Mandal, Numerical solution of a singular integro- differential equation, Appl. Math. Comput. 195 (1), 346–350, 2008.
  • [6] A. Chakrabarti, Applied Singular Integral Equations, Science Publishers, 2011.
  • [7] Z. Chen and Y. Lin, The exact solution of a linear integral equation with weakly singular kernel, J. Math. Anal. Appl. 344 (2), 726–734, 2008.
  • [8] S.M.A. Darwish, Weakly singular functional-integral equation in infinite dimensional Banach spaces, Appl. Math. Comput. 136 (1), 123–129, 2003.
  • [9] R. Estrada and R.P. Kanwal, Singular integral equations, Springer Science & Business Media, 2012.
  • [10] M.A. Golberg, Numerical Solution of Integral Equations, Springer US, 1990.
  • [11] P. Karczmarek, D. Pylak, and M.A. Sheshko, Application of Jacobi polynomials to approximate solution of a singular integral equation with Cauchy kernel, Appl. Math. Comput. 181 (1), 694–707, 2006.
  • [12] F.K. Keshi, B.P. Moghaddam, and A. Aghili, A numerical approach for solving a class of variable-order fractional functional integral equations, Comput. Appl. Math. 37 (4), 4821–4834, 2018.
  • [13] N. Khorrami, A.S. Shamloo, and B.P. Moghaddam, Nystrom method for solution of fredholm integral equations of the second kind under interval data, J. Intell. Fuzzy Syst. 36 (3), 2807–2816, 2019.
  • [14] D. Kincaid and E.W. Cheney, Numerical Analysis: Mathematics of Scientific Com- puting, Am. Math. Soc. 2009.
  • [15] S. Kumar and A.L. Sangal, Numerical solution of singular integral equations using cubic spline interpolations, Indian J. Pure Appl. Math. 35 (3), 415–421, 2004.
  • [16] P.K. Kythe and P. Puri, Computational Methods for Linear Integral Equations, Birkhauser Boston, 2002.
  • [17] I. Lifanov, L. Poltavskii, and G. Vainikko, Hypersingular Integral Equations and Their Applications, CRC Press, 2003.
  • [18] B.N. Mandal and G.H. Bera, Approximate solution of a class of singular integral equations of second kind, J. Comput. Appl. Math. 206 (1), 189–195, 2007.
  • [19] B.P. Moghaddam and J.A. Tenreiro Machado, Extended algorithms for approximating variable order fractional derivatives with applications, J. Sci. Comput. 71 (3), 1351– 1374, 2016.
  • [20] B.P. Moghaddam and J.A. Tenreiro Machado, A computational approach for the so- lution of a class of variable-order fractional integro-differential equations with weakly singular kernels, Fract. Calc. Appl. Anal. 20 (4), 1023–1042, 2017.
  • [21] P. Mokhtary, B.P. Moghaddam, A.M. Lopes, and J.A. Tenreiro Machado, A computational approach for the non-smooth solution of non-linear weakly singular Volterra integral equation with proportional delay, Numer. Algorithms 1–20, 2019. doi:10.1007/s11075-019-00712-y.
  • [22] N.I. Muskhelishvili, Singular integral equations: Boundary problems of functions the- ory and their application to mathematical physics, P. Noordhoff, 1953.
  • [23] A. Polyanin, Handbook of Integral Equations, CRC Press, 1998.
  • [24] A. Setia, Numerical solution of various cases of Cauchy type singular integral equa- tion, Appl. Math. Comput. 230, 200–207, 2014.
  • [25] M. Sheshko, Singular integral equations with Cauchy and Hilbert kernels and theirs approximated solutions, The Learned Society of the Catholic University of Lublin, Lublin, 2003.
  • [26] B.Q. Tang and X.F. Li, Solution of a class of Volterra integral equations with singular and weakly singular kernels, Appl. Math. Comput. 199 (2), 406–413, 2008.
  • [27] J.A. Tenreiro Machado, F. Mainardi, V. Kiryakova, and T. Atanacković, Fractional calculus: D’où venons-nous? Que sommes-nous? Où allons-nous?, Fract. Calc. Appl. Anal. 19 (5), 1074–1104, 2016.
  • [28] X. Jin, L.M. Keer, and Q. Wang, A practical method for singular integral equations of the second kind, Eng. Fract. Mech. 75 (5), 1005–1014, 2008.

A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials

Yıl 2020, , 974 - 983, 02.06.2020

Behrouz Parsa Moghaddam , J. A. Tenreiro Machado Parisa Sattari Shajari Zeynab Salamat Mostaghim

https://doi.org/10.15672/hujms.474938
Cited By: 3

Öz

A numerical algorithm based on Hermite polynomials for solving the Cauchy singular integral equation in the general form is presented. The Hermite polynomial interpolation of unknown functions is first introduced. The proposed technique is then used for approximating the solution of the Cauchy singular integral equation. This approach requires the solution of a system of linear algebraic equations. Two examples demonstrate the effectiveness of the proposed method.

Anahtar Kelimeler

Cauchy singular integral equation Hermite polynomials Numerical schemes Interpolation theory

Kaynakça

  • [1] M.A. Abdou and A.A. Nasr, On the numerical treatment of the singular integral equation of the second kind, Appl. Math. Comput. 143 (2-3), 373–380, 2003.
  • [2] K. Al-Khaled and M. Alquran, Convergence and norm estimates of Hermite interpo- lation at zeros of Chevyshev polynomials, SpringerPlus, 5 (1), 2016.
  • [3] A.A. Badr, Integro-differential equation with Cauchy kernel, J. Comput. Appl. Math. 134 (1-2), 191–199, 2001.
  • [4] P. Baratella and A.P. Orsi, A new approach to the numerical solution of weakly singular Volterra integral equations, J. Comput. Appl. Math. 163 (2), 401–418, 2004.
  • [5] S. Bhattacharya and B.N. Mandal, Numerical solution of a singular integro- differential equation, Appl. Math. Comput. 195 (1), 346–350, 2008.
  • [6] A. Chakrabarti, Applied Singular Integral Equations, Science Publishers, 2011.
  • [7] Z. Chen and Y. Lin, The exact solution of a linear integral equation with weakly singular kernel, J. Math. Anal. Appl. 344 (2), 726–734, 2008.
  • [8] S.M.A. Darwish, Weakly singular functional-integral equation in infinite dimensional Banach spaces, Appl. Math. Comput. 136 (1), 123–129, 2003.
  • [9] R. Estrada and R.P. Kanwal, Singular integral equations, Springer Science & Business Media, 2012.
  • [10] M.A. Golberg, Numerical Solution of Integral Equations, Springer US, 1990.
  • [11] P. Karczmarek, D. Pylak, and M.A. Sheshko, Application of Jacobi polynomials to approximate solution of a singular integral equation with Cauchy kernel, Appl. Math. Comput. 181 (1), 694–707, 2006.
  • [12] F.K. Keshi, B.P. Moghaddam, and A. Aghili, A numerical approach for solving a class of variable-order fractional functional integral equations, Comput. Appl. Math. 37 (4), 4821–4834, 2018.
  • [13] N. Khorrami, A.S. Shamloo, and B.P. Moghaddam, Nystrom method for solution of fredholm integral equations of the second kind under interval data, J. Intell. Fuzzy Syst. 36 (3), 2807–2816, 2019.
  • [14] D. Kincaid and E.W. Cheney, Numerical Analysis: Mathematics of Scientific Com- puting, Am. Math. Soc. 2009.
  • [15] S. Kumar and A.L. Sangal, Numerical solution of singular integral equations using cubic spline interpolations, Indian J. Pure Appl. Math. 35 (3), 415–421, 2004.
  • [16] P.K. Kythe and P. Puri, Computational Methods for Linear Integral Equations, Birkhauser Boston, 2002.
  • [17] I. Lifanov, L. Poltavskii, and G. Vainikko, Hypersingular Integral Equations and Their Applications, CRC Press, 2003.
  • [18] B.N. Mandal and G.H. Bera, Approximate solution of a class of singular integral equations of second kind, J. Comput. Appl. Math. 206 (1), 189–195, 2007.
  • [19] B.P. Moghaddam and J.A. Tenreiro Machado, Extended algorithms for approximating variable order fractional derivatives with applications, J. Sci. Comput. 71 (3), 1351– 1374, 2016.
  • [20] B.P. Moghaddam and J.A. Tenreiro Machado, A computational approach for the so- lution of a class of variable-order fractional integro-differential equations with weakly singular kernels, Fract. Calc. Appl. Anal. 20 (4), 1023–1042, 2017.
  • [21] P. Mokhtary, B.P. Moghaddam, A.M. Lopes, and J.A. Tenreiro Machado, A computational approach for the non-smooth solution of non-linear weakly singular Volterra integral equation with proportional delay, Numer. Algorithms 1–20, 2019. doi:10.1007/s11075-019-00712-y.
  • [22] N.I. Muskhelishvili, Singular integral equations: Boundary problems of functions the- ory and their application to mathematical physics, P. Noordhoff, 1953.
  • [23] A. Polyanin, Handbook of Integral Equations, CRC Press, 1998.
  • [24] A. Setia, Numerical solution of various cases of Cauchy type singular integral equa- tion, Appl. Math. Comput. 230, 200–207, 2014.
  • [25] M. Sheshko, Singular integral equations with Cauchy and Hilbert kernels and theirs approximated solutions, The Learned Society of the Catholic University of Lublin, Lublin, 2003.
  • [26] B.Q. Tang and X.F. Li, Solution of a class of Volterra integral equations with singular and weakly singular kernels, Appl. Math. Comput. 199 (2), 406–413, 2008.
  • [27] J.A. Tenreiro Machado, F. Mainardi, V. Kiryakova, and T. Atanacković, Fractional calculus: D’où venons-nous? Que sommes-nous? Où allons-nous?, Fract. Calc. Appl. Anal. 19 (5), 1074–1104, 2016.
  • [28] X. Jin, L.M. Keer, and Q. Wang, A practical method for singular integral equations of the second kind, Eng. Fract. Mech. 75 (5), 1005–1014, 2008.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Behrouz Parsa Moghaddam 0000-0003-4957-9028

J. A. Tenreiro Machado 0000-0003-4274-4879

Parisa Sattari Shajari 0000-0001-6014-4864

Zeynab Salamat Mostaghim 0000-0003-2352-976X

Yayımlanma Tarihi 2 Haziran 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Parsa Moghaddam, B., Tenreiro Machado, J. A., Sattari Shajari, P., Salamat Mostaghim, Z. (2020). A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials. Hacettepe Journal of Mathematics and Statistics, 49(3), 974-983. https://doi.org/10.15672/hujms.474938
AMA Parsa Moghaddam B, Tenreiro Machado JA, Sattari Shajari P, Salamat Mostaghim Z. A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials. Hacettepe Journal of Mathematics and Statistics. Haziran 2020;49(3):974-983. doi:10.15672/hujms.474938
Chicago Parsa Moghaddam, Behrouz, J. A. Tenreiro Machado, Parisa Sattari Shajari, ve Zeynab Salamat Mostaghim. “A Numerical Algorithm for Solving the Cauchy Singular Integral Equation Based on Hermite Polynomials”. Hacettepe Journal of Mathematics and Statistics 49, sy. 3 (Haziran 2020): 974-83. https://doi.org/10.15672/hujms.474938.
EndNote Parsa Moghaddam B, Tenreiro Machado JA, Sattari Shajari P, Salamat Mostaghim Z (01 Haziran 2020) A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials. Hacettepe Journal of Mathematics and Statistics 49 3 974–983.
IEEE B. Parsa Moghaddam, J. A. Tenreiro Machado, P. Sattari Shajari, ve Z. Salamat Mostaghim, “A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 3, ss. 974–983, 2020, doi: 10.15672/hujms.474938.
ISNAD Parsa Moghaddam, Behrouz vd. “A Numerical Algorithm for Solving the Cauchy Singular Integral Equation Based on Hermite Polynomials”. Hacettepe Journal of Mathematics and Statistics 49/3 (Haziran 2020), 974-983. https://doi.org/10.15672/hujms.474938.
JAMA Parsa Moghaddam B, Tenreiro Machado JA, Sattari Shajari P, Salamat Mostaghim Z. A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials. Hacettepe Journal of Mathematics and Statistics. 2020;49:974–983.
MLA Parsa Moghaddam, Behrouz vd. “A Numerical Algorithm for Solving the Cauchy Singular Integral Equation Based on Hermite Polynomials”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 3, 2020, ss. 974-83, doi:10.15672/hujms.474938.
Vancouver Parsa Moghaddam B, Tenreiro Machado JA, Sattari Shajari P, Salamat Mostaghim Z. A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials. Hacettepe Journal of Mathematics and Statistics. 2020;49(3):974-83.

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Spectral Methods For Hammerstein Integral Equations with Nonsmooth Kernels
International Journal of Computational Methods
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