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Year 2023, Volume: 44 Issue: 3, 561 - 566, 29.09.2023

Taiye Oyedepo , Abayomi Ayoade , Ganiyu Ajileye Nneoma Joyce Ikechukwu

https://doi.org/10.17776/csj.1267158
Cited By: 1

Abstract

References

  • [1] Behiry S.H, Mohamed S.I., Solving high-order nonlinear Volterra-Fredholm integro-differential equations by differential transform method, Natural Science, 4(8)(2012), 581-587.
  • [2] Maleknejad K., Basirat B., E. Hashemizadeh E., A Bernstein operational matrix approach for solving a system of high order linear Volterra–Fredholm integro-differential equations, Mathematical Computational Modell, 55(3) (2012) 1363–1372.
  • [3] Mishra V.N., Marasi H.R., Shabanian H. Sahlan, M.N., Solution of Volterra –Fredholm integro-differential equations using Chebyshev collocation method, Global Journal Technology and Optimization, (1) (2017) 1-4.
  • [4] Deniz E., Nurcan B.S. Numerical solution of high-order linear Fredholm integro-differential equations by Lucas Collocation method. International Journal of Informatics and Applied Mathematics & Statistics, 5(2) (2022) 24–40.
  • [5] Deniz E., Nurcan B.S. Numerical solution of high-order linear Fredholm integro-differential equations by Lucas Collocation method. International Journal of Informatics and Applied Mathematics, & Statistics, 5(2) (2022) 24–40.
  • [6] Shoushan A.F. Al-Humedi H.O. The numerical solutions of integro-differential equations by Euler polynomials with least squares method. Palarch’s Journal Of Archaeology Of Egypt/Egyptology Journals, 18(4) (2021) 1740–1753.
  • [7] Hashim I. Adomian decomposition method for solving BVPs for fourth-order integro-differential equations, Journal of Computer and Applied Mathematics, 193 (2006) 658-664.
  • [8] Saadati R., Raftari B., Adibi H. S.M., Vaezpour S.M., Shakeri S., A comparison between the Variational Iteration method and Trapezoidal rule for solving linear integro-differential equations, World Applied Sciences Journal, 4(3) (2008) 321–325.
  • [9] Sweilam N.H., Fourth order integro-differential equations using variational iteration method, Computer Mathematics Applications, 54 (2007) 1086-1091.
  • [10] Acar N.I., Daşcıoğlu A., Projection method for linear Fredholm–Volterra integro-differential equations, Journal of Taibah University for Science, 13(1) (2019) 644-650.
  • [11] Akyüz-DaGcJoLlu A., Acar N., Güler C., Bernstein collocation method for solving nonlinear Fredholm-Volterra integro differential equations in the most general form, Journal of Applied Mathematics, 134272 (2014) 1-8.
  • [12] Berenguer M.I., Gamez D., Opez Linares, A.J.L., Fixed-point iterative algorithm for the linear Fredholm-Volterra integro-differential equation, Journal of Computational and Applied Mathematics, 370894 (2012) 1-12.
  • [13] Yüksel G., Gülsu M. Sezer, M. A Chebyshev polynomial approach for high-order linear Fredholm-Volterra integro-differential equations, Gazi University Journal of Science, 25(2) (2012) 393-401.
  • [14] Yuzbası S. A collocation method based on Bernstein polynomials to solve nonlinear Fredholm–Volterra integro-differential equations, Applied Mathematics Computation, 273 (2016) 142–154.
  • [15] Loh R.J., Phang C., A new numerical scheme for solving system of Volterra integro-differential equation, Alexandria Enginerring Journal, 57(2) (2018) 1117-1124.
  • [16] Gumgum S., Savaşaneril N.B.,, Kurkcu O.K.,, Sezer M.S., Lucas polynomial solution of nonlinear differential equations with variable delays, Hacettepe Journal of Mathematics & Statistics, 49(2) (2020) 553–564.
  • [17] Sakran M.R.A., Numerical solutions of integral and integro -differential equations using Chebyshev polynomial of the third kind, Applied Mathematics and Computation, 5 (2019) 66 -82.
  • [18] Ayinde A.M, James A.A., Ishaq A.A. and Oyedepo T. A new numerical approach using Chebyshev third kind polynomial for solving integro-differential equations of higher order, Gazi University Journal of Science, Part A, 9(3) (2022) 259-266.
  • [19] Oyedepo T., Ayoade A.A., Oluwayemi M.O.,Pandurangan R., Solution of Volterra-Fredholm integro- differential equations using the Chebyshev computational approach, International Conference on Science, Engineering and Business for Sustainable Development Goals (SEB-SDG),Omu-Aran, Nigeria, 1 (2023) 1-6.
  • [20] Akgonullu N., Şahin N., Sezer M., A Hermite collocation method for the approximation solutions of higher-order linear Fredholm integro-differential equations, Numerical Methods for Partial Differential Equations, 27(6) (2011) 1707-1721.
  • [21] Aruchunan E., Sulaiman J., Numerical solution of second order linear Fredholm integro-differential equations using generalized minimal residual method, American, Journal of the Applied Sciences, 7(6) (2010) 780–783.
  • [22] Jalius C., Abdul Z., Majid, Numerical solution of second-Order Fredholm integro-differential equations with boundary conditions by Quadrature-Difference method, Hindawi Journal of Applied Mathematics, 2645097 (2017) 1-5.
  • [23] Vahidi A.R., Babolian E., AsadiCordshooli G., Azimzadeh, Z., Numerical solution of Fredholm integro-differential equation by Adomian’s decomposition method, International Journal of Mathematical Analysis, 3 (2009) 1769–1773.
  • [24] Bhrawy A., Tohidi E., Soleymani F., A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals, Appl. Math. Comput., 219(2) (2012) 482-497.

Legendre Computational Algorithm for Linear Integro-Differential Equations

Year 2023, Volume: 44 Issue: 3, 561 - 566, 29.09.2023

Taiye Oyedepo , Abayomi Ayoade , Ganiyu Ajileye Nneoma Joyce Ikechukwu

https://doi.org/10.17776/csj.1267158
Cited By: 1

Abstract

This work presents a collocation computational algorithm for solving linear Integro-Differential Equations (IDEs) of the Fredholm and Volterra types. The proposed method utilizes shifted Legendre polynomials and breaks down the problem into a series of linear algebraic equations. The matrix inversion technique is then employed to solve these equations. To validate the effectiveness of the suggested approach, the authors examined three numerical examples. The results obtained from the proposed method were compared with those reported in the existing literature. The findings demonstrate that the proposed algorithm is not only accurate but also efficient in solving linear IDEs. In order to present the results, the study employs tables and figures. These graphical representations aid in displaying the numerical outcomes obtained from the algorithm. All calculations were performed using Maple 18 software.

Keywords

Legendre polynomials Fredholm and Volterra integro-differential equations Approximate solution

References

  • [1] Behiry S.H, Mohamed S.I., Solving high-order nonlinear Volterra-Fredholm integro-differential equations by differential transform method, Natural Science, 4(8)(2012), 581-587.
  • [2] Maleknejad K., Basirat B., E. Hashemizadeh E., A Bernstein operational matrix approach for solving a system of high order linear Volterra–Fredholm integro-differential equations, Mathematical Computational Modell, 55(3) (2012) 1363–1372.
  • [3] Mishra V.N., Marasi H.R., Shabanian H. Sahlan, M.N., Solution of Volterra –Fredholm integro-differential equations using Chebyshev collocation method, Global Journal Technology and Optimization, (1) (2017) 1-4.
  • [4] Deniz E., Nurcan B.S. Numerical solution of high-order linear Fredholm integro-differential equations by Lucas Collocation method. International Journal of Informatics and Applied Mathematics & Statistics, 5(2) (2022) 24–40.
  • [5] Deniz E., Nurcan B.S. Numerical solution of high-order linear Fredholm integro-differential equations by Lucas Collocation method. International Journal of Informatics and Applied Mathematics, & Statistics, 5(2) (2022) 24–40.
  • [6] Shoushan A.F. Al-Humedi H.O. The numerical solutions of integro-differential equations by Euler polynomials with least squares method. Palarch’s Journal Of Archaeology Of Egypt/Egyptology Journals, 18(4) (2021) 1740–1753.
  • [7] Hashim I. Adomian decomposition method for solving BVPs for fourth-order integro-differential equations, Journal of Computer and Applied Mathematics, 193 (2006) 658-664.
  • [8] Saadati R., Raftari B., Adibi H. S.M., Vaezpour S.M., Shakeri S., A comparison between the Variational Iteration method and Trapezoidal rule for solving linear integro-differential equations, World Applied Sciences Journal, 4(3) (2008) 321–325.
  • [9] Sweilam N.H., Fourth order integro-differential equations using variational iteration method, Computer Mathematics Applications, 54 (2007) 1086-1091.
  • [10] Acar N.I., Daşcıoğlu A., Projection method for linear Fredholm–Volterra integro-differential equations, Journal of Taibah University for Science, 13(1) (2019) 644-650.
  • [11] Akyüz-DaGcJoLlu A., Acar N., Güler C., Bernstein collocation method for solving nonlinear Fredholm-Volterra integro differential equations in the most general form, Journal of Applied Mathematics, 134272 (2014) 1-8.
  • [12] Berenguer M.I., Gamez D., Opez Linares, A.J.L., Fixed-point iterative algorithm for the linear Fredholm-Volterra integro-differential equation, Journal of Computational and Applied Mathematics, 370894 (2012) 1-12.
  • [13] Yüksel G., Gülsu M. Sezer, M. A Chebyshev polynomial approach for high-order linear Fredholm-Volterra integro-differential equations, Gazi University Journal of Science, 25(2) (2012) 393-401.
  • [14] Yuzbası S. A collocation method based on Bernstein polynomials to solve nonlinear Fredholm–Volterra integro-differential equations, Applied Mathematics Computation, 273 (2016) 142–154.
  • [15] Loh R.J., Phang C., A new numerical scheme for solving system of Volterra integro-differential equation, Alexandria Enginerring Journal, 57(2) (2018) 1117-1124.
  • [16] Gumgum S., Savaşaneril N.B.,, Kurkcu O.K.,, Sezer M.S., Lucas polynomial solution of nonlinear differential equations with variable delays, Hacettepe Journal of Mathematics & Statistics, 49(2) (2020) 553–564.
  • [17] Sakran M.R.A., Numerical solutions of integral and integro -differential equations using Chebyshev polynomial of the third kind, Applied Mathematics and Computation, 5 (2019) 66 -82.
  • [18] Ayinde A.M, James A.A., Ishaq A.A. and Oyedepo T. A new numerical approach using Chebyshev third kind polynomial for solving integro-differential equations of higher order, Gazi University Journal of Science, Part A, 9(3) (2022) 259-266.
  • [19] Oyedepo T., Ayoade A.A., Oluwayemi M.O.,Pandurangan R., Solution of Volterra-Fredholm integro- differential equations using the Chebyshev computational approach, International Conference on Science, Engineering and Business for Sustainable Development Goals (SEB-SDG),Omu-Aran, Nigeria, 1 (2023) 1-6.
  • [20] Akgonullu N., Şahin N., Sezer M., A Hermite collocation method for the approximation solutions of higher-order linear Fredholm integro-differential equations, Numerical Methods for Partial Differential Equations, 27(6) (2011) 1707-1721.
  • [21] Aruchunan E., Sulaiman J., Numerical solution of second order linear Fredholm integro-differential equations using generalized minimal residual method, American, Journal of the Applied Sciences, 7(6) (2010) 780–783.
  • [22] Jalius C., Abdul Z., Majid, Numerical solution of second-Order Fredholm integro-differential equations with boundary conditions by Quadrature-Difference method, Hindawi Journal of Applied Mathematics, 2645097 (2017) 1-5.
  • [23] Vahidi A.R., Babolian E., AsadiCordshooli G., Azimzadeh, Z., Numerical solution of Fredholm integro-differential equation by Adomian’s decomposition method, International Journal of Mathematical Analysis, 3 (2009) 1769–1773.
  • [24] Bhrawy A., Tohidi E., Soleymani F., A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals, Appl. Math. Comput., 219(2) (2012) 482-497.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Taiye Oyedepo 0000-0001-9063-8806

Abayomi Ayoade 0000-0003-3470-0147

Ganiyu Ajileye 0000-0002-4161-686X

Nneoma Joyce Ikechukwu 0000-0001-9049-3037

Publication Date September 29, 2023
Submission Date March 18, 2023
Acceptance Date September 7, 2023
Published in Issue Year 2023Volume: 44 Issue: 3

Cite

APA Oyedepo, T., Ayoade, A., Ajileye, G., Ikechukwu, N. J. (2023). Legendre Computational Algorithm for Linear Integro-Differential Equations. Cumhuriyet Science Journal, 44(3), 561-566. https://doi.org/10.17776/csj.1267158

Cited By

Simulation of Two-Step Block Approach for Solving Oscillatory Differential Equations
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https://doi.org/10.17776/csj.1345303
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