Araştırma Makalesi
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Yıl 2020, Cilt: 17 Sayı: 1, 41 - 51, 01.05.2020

Morufu Oyedunsi Olayiwola A. F. Adebısı Y. S. Arowolo

Öz

Kaynakça

  • [1] Volterra V. Theory of Functionals and of Integral and Integro-differential Equations, Dover Publications,(2005).
  • [2] Maleknejad, K. and Agazadeh, N., Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, Appl. Math. Compu., 161, (2005), 915-922.
  • [3] Brunner, H., The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes, Appl. Math. Compu., 45, (1985), 417-437.
  • [4] Brunner, H., On the Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations by collocation Methods, SIAM Jour. Numer. Anal., 27, (1990), 987-1000.
  • [5] Maleknejad, K. Sohrabi, S. and Rostami, Y., Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polyomials, Appl. Math. Compu., 188,(2007), 123-128.
  • [6] Rabbani, M., Maleknejad, K. and Aghazadeh, N., Numerical computational solution of the Volterra integral equations system of the second kind by using an expansion method, Appl.Math. Compu., 187, (2007), 1143-1146.
  • [7] Maleknejad, K., Hashemizadeh, E. and Ezzati, R., A new approach to the numerical solution of Volterra integral equations by using Bernstein’s approximation, Commu. Nonlinear Sci. Num. Simul., 16, (2011), 647-655.
  • [8] Wazwaz, A., Two methods for solving integral equations, Appl. Math. Compu., 77, (1996), 79-89.
  • [9] Wazwaz, A., Linear and Nonlinear Integral Equations: Methods and Applications, Higher education press, (2011), Springer.
  • [10] Rashed, M., Lagrange interpolation to compute the numerical solutions of differential, integral and integro-differential equations, Appl. Math. Compu., 151, (2004), 869-878.
  • [11] Hashim, I. Adomian decomposition method for solving BVPs for fourth-order integro-differential equations, Jour. Compu. Appl. Math., 193, (2006), 658-664.
  • [12] Maleknejad, K. and Mahmoudi, Y., Taylor polynomial solution of high-order nonlinear Volterra-Fredholm integro-differential equations, Appl. Math. Compu., 145, (2003), 641-653.
  • [13] Maleknejad, K. Mirzaee, F. and Abbasbandy, S. Solving linear integro-differential equations system by using rationalized Haar function method, Appl. Math. Compu., 155, (2005), 317- 328.
  • [14] Darnaia, P. and Ebadian, A., A method for the numerical solution of the integro-differential equations, Appl. Math. Compu., 188, (2007), 657-668.
  • [15] Sweilam, N., Fourth order integro-differential equations using variational iteration method, Compu. Math. Appl., 54, (2007), 1086-1091.
  • [16] Hosseini, S. and Shahmorad, S., Numerical solution of a class of Integro-Differential equations by the Tau Method with an error estimation, Appl. Math. Compu., 136, (2003), 559-570.
  • [17] Olayiwola, M.O, Solutions to Emden Fowler Type Equations by Variational Iteration Method. Cankaya University,Journal of Science and Engineering.16(2), (2019), 001-009.
  • [18] Cardone, A, Conte, D.D’Ambrosio R. and Parameter, B., Collocation Methods for Volterra Integral and Integro-Differential Equations: A Review, Axioms, 7, (2018), 45-61; doi:10.3390/axioms7030045.
  • [19] Taiwo, O.A and Adebisi, A.F. Multiple Perturbed Collocation Tau method for special class of higher order linear Fredholm and Volterra Integro-differential Equations. Pro-Journal of Physical Science Research (PPSR). 2(3), (2014), 13-22.
  • [20] Adewunmi, A.O. Tau Homotopy and embedded Perturbed integral Collocation Methods for Solving Boundary Valued Problems.Comm.. B. Nonlinear Sci. Numerical Simulation. 14, (2014), 3530-3536.The Numerical Solution of Second Order, BVP, J of NAMP, 10, 293-298.

Application of Legendre Polynomial Basis Function on the Solution of Volterra Integro-Differential Equations Using Collocation Method

Yıl 2020, Cilt: 17 Sayı: 1, 41 - 51, 01.05.2020

Morufu Oyedunsi Olayiwola A. F. Adebısı Y. S. Arowolo

Öz

In this paper, we presented an efficient numerical method of solving Volterra integro-differential equations by applying Legendre as basis function for the solution of initial value problem of Integro-differential equations. We assumed appropriate solutions in terms of Legendre polynomial as basis function which was substituted into the class of integro-differential equations considered. This transformed the integro-differential equations and the given initial conditions into matrix equations. By collocating at point corresponding to N- systems of equations, the results obtained for some numerical examples justified the efficiency and reliability of the proposed method.

Anahtar Kelimeler

Collocation method Legendre polynomial basis function Volterra Integro-differential equations

Kaynakça

  • [1] Volterra V. Theory of Functionals and of Integral and Integro-differential Equations, Dover Publications,(2005).
  • [2] Maleknejad, K. and Agazadeh, N., Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, Appl. Math. Compu., 161, (2005), 915-922.
  • [3] Brunner, H., The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes, Appl. Math. Compu., 45, (1985), 417-437.
  • [4] Brunner, H., On the Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations by collocation Methods, SIAM Jour. Numer. Anal., 27, (1990), 987-1000.
  • [5] Maleknejad, K. Sohrabi, S. and Rostami, Y., Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polyomials, Appl. Math. Compu., 188,(2007), 123-128.
  • [6] Rabbani, M., Maleknejad, K. and Aghazadeh, N., Numerical computational solution of the Volterra integral equations system of the second kind by using an expansion method, Appl.Math. Compu., 187, (2007), 1143-1146.
  • [7] Maleknejad, K., Hashemizadeh, E. and Ezzati, R., A new approach to the numerical solution of Volterra integral equations by using Bernstein’s approximation, Commu. Nonlinear Sci. Num. Simul., 16, (2011), 647-655.
  • [8] Wazwaz, A., Two methods for solving integral equations, Appl. Math. Compu., 77, (1996), 79-89.
  • [9] Wazwaz, A., Linear and Nonlinear Integral Equations: Methods and Applications, Higher education press, (2011), Springer.
  • [10] Rashed, M., Lagrange interpolation to compute the numerical solutions of differential, integral and integro-differential equations, Appl. Math. Compu., 151, (2004), 869-878.
  • [11] Hashim, I. Adomian decomposition method for solving BVPs for fourth-order integro-differential equations, Jour. Compu. Appl. Math., 193, (2006), 658-664.
  • [12] Maleknejad, K. and Mahmoudi, Y., Taylor polynomial solution of high-order nonlinear Volterra-Fredholm integro-differential equations, Appl. Math. Compu., 145, (2003), 641-653.
  • [13] Maleknejad, K. Mirzaee, F. and Abbasbandy, S. Solving linear integro-differential equations system by using rationalized Haar function method, Appl. Math. Compu., 155, (2005), 317- 328.
  • [14] Darnaia, P. and Ebadian, A., A method for the numerical solution of the integro-differential equations, Appl. Math. Compu., 188, (2007), 657-668.
  • [15] Sweilam, N., Fourth order integro-differential equations using variational iteration method, Compu. Math. Appl., 54, (2007), 1086-1091.
  • [16] Hosseini, S. and Shahmorad, S., Numerical solution of a class of Integro-Differential equations by the Tau Method with an error estimation, Appl. Math. Compu., 136, (2003), 559-570.
  • [17] Olayiwola, M.O, Solutions to Emden Fowler Type Equations by Variational Iteration Method. Cankaya University,Journal of Science and Engineering.16(2), (2019), 001-009.
  • [18] Cardone, A, Conte, D.D’Ambrosio R. and Parameter, B., Collocation Methods for Volterra Integral and Integro-Differential Equations: A Review, Axioms, 7, (2018), 45-61; doi:10.3390/axioms7030045.
  • [19] Taiwo, O.A and Adebisi, A.F. Multiple Perturbed Collocation Tau method for special class of higher order linear Fredholm and Volterra Integro-differential Equations. Pro-Journal of Physical Science Research (PPSR). 2(3), (2014), 13-22.
  • [20] Adewunmi, A.O. Tau Homotopy and embedded Perturbed integral Collocation Methods for Solving Boundary Valued Problems.Comm.. B. Nonlinear Sci. Numerical Simulation. 14, (2014), 3530-3536.The Numerical Solution of Second Order, BVP, J of NAMP, 10, 293-298.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Morufu Oyedunsi Olayiwola 0000-0001-6101-1203

A. F. Adebısı Bu kişi benim

Y. S. Arowolo Bu kişi benim

Yayımlanma Tarihi 1 Mayıs 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 17 Sayı: 1

Kaynak Göster

APA Olayiwola, M. O., Adebısı, A. F., & Arowolo, Y. S. (2020). Application of Legendre Polynomial Basis Function on the Solution of Volterra Integro-Differential Equations Using Collocation Method. Cankaya University Journal of Science and Engineering, 17(1), 41-51.
AMA Olayiwola MO, Adebısı AF, Arowolo YS. Application of Legendre Polynomial Basis Function on the Solution of Volterra Integro-Differential Equations Using Collocation Method. CUJSE. Mayıs 2020;17(1):41-51.
Chicago Olayiwola, Morufu Oyedunsi, A. F. Adebısı, ve Y. S. Arowolo. “Application of Legendre Polynomial Basis Function on the Solution of Volterra Integro-Differential Equations Using Collocation Method”. Cankaya University Journal of Science and Engineering 17, sy. 1 (Mayıs 2020): 41-51.
EndNote Olayiwola MO, Adebısı AF, Arowolo YS (01 Mayıs 2020) Application of Legendre Polynomial Basis Function on the Solution of Volterra Integro-Differential Equations Using Collocation Method. Cankaya University Journal of Science and Engineering 17 1 41–51.
IEEE M. O. Olayiwola, A. F. Adebısı, ve Y. S. Arowolo, “Application of Legendre Polynomial Basis Function on the Solution of Volterra Integro-Differential Equations Using Collocation Method”, CUJSE, c. 17, sy. 1, ss. 41–51, 2020.
ISNAD Olayiwola, Morufu Oyedunsi vd. “Application of Legendre Polynomial Basis Function on the Solution of Volterra Integro-Differential Equations Using Collocation Method”. Cankaya University Journal of Science and Engineering 17/1 (Mayıs 2020), 41-51.
JAMA Olayiwola MO, Adebısı AF, Arowolo YS. Application of Legendre Polynomial Basis Function on the Solution of Volterra Integro-Differential Equations Using Collocation Method. CUJSE. 2020;17:41–51.
MLA Olayiwola, Morufu Oyedunsi vd. “Application of Legendre Polynomial Basis Function on the Solution of Volterra Integro-Differential Equations Using Collocation Method”. Cankaya University Journal of Science and Engineering, c. 17, sy. 1, 2020, ss. 41-51.
Vancouver Olayiwola MO, Adebısı AF, Arowolo YS. Application of Legendre Polynomial Basis Function on the Solution of Volterra Integro-Differential Equations Using Collocation Method. CUJSE. 2020;17(1):41-5.