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Numerical solution of two-dimensional Fredholm integro-differential equations by Chebyshev integral operational matrix method

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents the Chebyshev Integral Operational Matrix Method (CIOMM) for the numerical solution of two-dimensional Fredholm Integro-Differential Equations (2D-FIDEs). The process of the method is obtaining the operational matrix of integration by evaluating a 2D integral of 2D Chebyshev polynomial basis functions and assuming approximate solutions of the 2D-FIDEs as a truncated 2D Chebyshev series. This leads to a system of linear algebraic equations which are solved to obtain the values of the unknown constants using Maple 18. Some numerical problems are solved to illustrate the practicability of the method.
Rocznik
Strony
29--40
Opis fizyczny
Bibliogr. 23 poz., rys., tab.
Twórcy
  • Department of Mathematics, National Open University of Nigeria, Abuja, Nigeria
  • Department of Mathematics University of Ilorin, Ilorin, Nigeria
  • Department of Mathematical Sciences, Osun State University, Osogbo, Nigeria
  • Department of Mathematics University of Ilorin, Ilorin, Nigeria
Bibliografia
  • [1] Basseem, M. (2015). Degenerate kernel method for three dimension nonlinear integral equations of the second kind. Universal Journal of Integral Equation, 3, 61-66.
  • [2] Carutasu, V. (2001). Numerical solution of two-dimensional nonlinear Fredholm integral equations of the second kind by spline functions. General Mathematics, 9, 31-48.
  • [3] Ziyaee, F., & Tari, A. (2014). Regularization method for the two-dimensional Fredholm integral equations of the first kind. International Journal of Nonlinear Science, 18(3), 189-194.
  • [4] Ziyaee, F., & Tari, A. (2015). Differential transform method for solving the two-dimensional integral equations. Applications and Applied Mathematics, 10(2), 852-863.
  • [5] Avazzadeh, Z., & Heydari, M. (2012). Chebyshev polynomial for solving two dimensional linear and nonlinear integral equations of the second kind. Computational and Applied Mathematics, 31(1), 127-142.
  • [6] Taiwo, O.A., & Abubakar, A. (2013). Integral collocation approximation methods for the numerical solution of linear integro-differential equations. IOSR Journal of Mathematics, 8(5), 1-14.
  • [7] Taiwo, O.A., Jimoh, A.K., & Bello, A.K. (2014). Comparison of some numerical methods for the solutions of first and second orders linear integro-differential equations. American Journal of Engineering Research, 3(1), 245-250.
  • [8] Uwaheren, O.A., Adebisi, A.F., Olotu, O.T., Etuk, M.O., & Peter, O.J. (2021). Legendre Galerkin method for solving fractional integro-differential equations of Fredholm type. The Aligarh Bulletin of Mathematics, 40(1), 1-13.
  • [9] Yousefi, S.A., & Behroozifar, M. (2010). Operational matrices of Berstein polynomials and their applications. International Journal of Systems Science, 41(6), 709-716.
  • [10] Mirzaee, F. (2013). Solving a class of non-linear Volterra integral equations by using two-dimensional triangular orthogonal functions. Journal of Mathematical Modeling, 1(1), 28-40.
  • [11] Khajehnasiri, A.A. (2016). Numerical solution of non-linear 2D Volterra-Fredholm integro- differential equations by two-dimensional triangular function. International Journal of Applied Computational Mathematics, 2, 575-591.
  • [12] Yuzbasi, S., & Ismailov, N. (2018). An operational matrix method for solving linear Fredholm- Volterra integro-differential equations. Turkish Journal of Mathematics, 42, 243-256.
  • [13] Rivaz, A., Samane J., & Yousefi, F. (2015). Two-dimensional Chebyshev polynomials for solving two-dimensional integro-differential equations. Cankaya University Journal of Science and Engineering, 12(2), 1-11.
  • [14] Mohamed, D. (2016). Shifted Chebyshev polynomials for solving three-dimensional Volterra integral equations of the second kind. arXiv:1609.08539v1.
  • [15] Kumar, P., & Qureshi, S. (2020). Laplace-Carson integral transform for exact solutions of non-integer order initial value problems with Caputo operator. Journal of Applied Mathematics and Computational Mechanics, 19(1).
  • [16] Qureshi, S., & Atangana, A. (2020). Fractal-fractional differentiation for the modelling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data. Chaos, Solitons & Fractals, 136, 109812.
  • [17] Qureshi, S. (2020). Monotonically decreasing behavior of measles epidemic well captured by Atangana-Baleanu-Caputo fractional operator under real measles data of Pakistan. Chaos, Solitons & Fractals, 131, 109478
  • [18] Qureshi, S.,& Yusuf, A. (2019). Fractional derivatives applied to MSEIR problems: Comparative study with real world data. The European Physical Journal Plus, 134(4), 1-13.
  • [19] Qureshi, S. (2021). Fox H-functionsas exact solutions for Caputo type mass springdamper system under Sumudu transform. Journal of Applied Mathematics and Computational Mechanics, 20(1), 83- 89.
  • [20] Demongeot, J., Griette, Q., & Magal P. (2020). SI epidemic model applied to COVID-19 data in mainland China. R. Soc. Open Sci. 7201878201878, doi: 10.1098/rsos.201878.
  • [21] Ramosa, H., & Vigo-Aguiar, J. (2007). Variable-Stepsize Chebyshev-type methods for the integration of second-order I.V.P.s. Journal of Computational and Applied Mathematics, 204, 102-113.
  • [22] Sastry, S.S. (2006). Introductory Methods of Numerical Analysis. Prentice-Hall of India Private Limited.
  • [23] Mason, J.C., & Handscomb, D.C. (2003). Chebyshev Polynomials. Florida: CRC Press.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fceeed34-fb47-41c3-8ebd-22e45ac43354
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