Abdullahi Muhammed AYINDE, Adewale Adeyemi JAMES, Ajimoti Adam ISHAQ, Taiye OYEDEPO

A New Numerical Approach Using Chebyshev Third Kind Polynomial for Solving Integrodifferential Equations of Higher Order

There are several classifications of linear Integral Equations. Some of them include; Voltera Integral Equations, Fredholm Linear Integral Equations, Fredholm-Voltera Integrodifferential. In the past, solutions of higher-order Fredholm-Volterra Integrodifferential Equations [FVIE] have been presented. However, this work uses a computational techniques premised on the third kind Chebyshev polynomials method. The performance of the results for distinctive degrees of approximation (M) of the trial solution is cautiously studied and comparisons have been additionally made between the approximate/estimated and exact/definite solution at different intervals of the problems under consideration. Modelled Problems have been provided to illustrate the performance and relevance of the techniques. However, it turned out that as M increases, the outcomes received after every iteration get closer to the exact solution in all of the problems considered. The results of the experiments are therefore visible from the tables of errors and the graphical representation presented in this work.

Keywords:

Degree of Approximant Exact Solution, Third Kind Chebyshev Polynomial, Trial Solution, Volterra-Fredholm Integrodifferential Equations,

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Adebisi, A. F., Ojurongbe, T. A., Okunlola, K. A., & Peter, O. J. (2021). Application of Chebyshev polynomial basis function on the solution of Volterra integro-differential equations using Galerkin method. Mathematics and Computational Sciences, 2(4), 41-51. doi:10.30511/mcs.2021.540133.1047
Akgonullu, N., Şahin, N., & Sezer, M. (2011). A Hermite Collocation Method For The Approximation Solutions of Higher-Order Linear Fredholm Integrodifferential equations. Numerical Methods for Partial Differential Equations, 27(6), 1707-1721. doi:10.1002/num.20604
Eslahchi, M. R., Mehdi, D., & Sanaz, A. (2012). The third and fourth kinds of Chebyshev polynomials and best uniform approximation. Mathematical and Computer Modelling, 55(5-6), 1746-1762. doi:10.1016/j.mcm.2011.11.023
Gulsu, M., Ozturk, Y., & Sezer, M. (2010). A New Collocation Method for Solution of Mixed Linear Integrodifferential equations. Applied Mathematics and Computation, 216(7), 2183-2198. doi:10.1016/j.amc.2010.03.054
Kurt, N., & Sezer, M. (2008). Polynomial solution of high-order linear Fredholm integro-differential equations with constant coefficients. Journal of the Franklin Institute, 345(8), 839-850. doi:10.1016/j.jfranklin.2008.04.016
Loh, R. J., & Phang, C. (2018). A new numerical scheme for solving system of Volterra integro-differential equation. Alexandria Enginerring Journal, 57(2), 1117-1124. doi:10.1016/j.aej.2017.01.021
Lotfi, M., & Alipanah, A. (2020). Legendre spectral element method for solving Volterra-integro differential equations. Results in Applied Mathematics, 7, 100116. doi:10.1016/j.rinam.2020.100116
Rabiei, F., Abd Hamid, F., Abd Majid, Z., & Ismail, F. (2019). Numerical solutions of Volterra integro-differential equations using General Linear Method. Numerical Algebra, Control and Optimization, 9(4), 433-444. doi:10.3934/naco.2019042
Rashed, M. T. (2004). Lagrange interpolation to compute the numerical solutions differential, Integral, and Integrodifferential equations. Applied Mathematics and Computation, 151(3), 869-878, doi:10.1016/S0096-3003(03)00543-5
Rashidinia, J., & Tahmasebi, A. (2012). Taylor Series Method for the System of Linear Volterra Integro-differential Equations. Journal of Mathematics and Computer Science, 4(3), 331-343. doi:10.22436/jmcs.04.03.06
Sakran, M. R. A. (2019). Numerical solutions of integral and integro-differential equations using Chebyshev polynomial of the third kind. Applied Mathematics and Computation, 35, 66-82. doi:10.1016/j.amc.2019.01.030
Samaher, M. Y. (2021). Reliable Iterative Method for solving Volterra - Fredholm Integro Differential Equations. Al-Qadisiyah Journal of Pure Science, 26(2), 1-11. doi:10.29350/qjps.2021.26.2.1262
Sezer, M., & Gulsu, M. (2005). Polynomial solution of the most general linear Fredholm integrodifferential–difference equations by means of Taylor matrix method. Complex Variables Theory and Application An International Journal, 50(5), 367-382. doi:10.1080/02781070500128354
Shah, K., & Singh, T. (2015). Solution of second kind Volterra integral and integro-differential equation by Homotopy analysis method. International Journal of Mathematical Archive, 6(4), 49-59.
Taiwo, O. A., & Fesojaye, M. O. (2015). Perturbation Least-Squares Chebyshev method for solving fractional order integro-differential equations. Theoretical Mathematics and Applications, 5(4), 37-47.
Wazwaz, A. M. (2010). The combined Laplace transform–Adomian decomposition method for handling nonlinear Volterra integro–differential equations. Applied Mathematics and Computation, 216(4), 1304-1309. doi:10.1016/j.amc.2010.02.023
Wazwaz, A. M. (2011). Linear and Nonlinear Integral Equations Methods and Applications. Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg.
Yusufoglu (Agadjanov), E. (2007). An efficient algorithm for solving Integrodifferential equations system. Applied Mathematics and Computation, 192(1), 51-55. doi:10.1016/j.amc.2007.02.134

Gazi University Journal of Science Part A: Engineering and Innovation-Cover

Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2013
Yayıncı: Gazi Üniversitesi, Fen Bilimleri Enstitüsü

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