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Year 2020, Volume: 17 Issue: 1, 41 - 51, 01.05.2020

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

Abstract

References

  • [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

Year 2020, Volume: 17 Issue: 1, 41 - 51, 01.05.2020

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

Abstract

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.

Keywords

Collocation method Legendre polynomial basis function Volterra Integro-differential equations

References

  • [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.
There are 20 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Morufu Oyedunsi Olayiwola 0000-0001-6101-1203

A. F. Adebısı This is me

Y. S. Arowolo This is me

Publication Date May 1, 2020
Published in Issue Year 2020 Volume: 17 Issue: 1

Cite

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. May 2020;17(1):41-51.
Chicago Olayiwola, Morufu Oyedunsi, A. F. Adebısı, and 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, no. 1 (May 2020): 41-51.
EndNote Olayiwola MO, Adebısı AF, Arowolo YS (May 1, 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, and Y. S. Arowolo, “Application of Legendre Polynomial Basis Function on the Solution of Volterra Integro-Differential Equations Using Collocation Method”, CUJSE, vol. 17, no. 1, pp. 41–51, 2020.
ISNAD Olayiwola, Morufu Oyedunsi et al. “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 (May 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 et al. “Application of Legendre Polynomial Basis Function on the Solution of Volterra Integro-Differential Equations Using Collocation Method”. Cankaya University Journal of Science and Engineering, vol. 17, no. 1, 2020, pp. 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.