Nonlinear second order systems of Fredholm integro-differential equations

被引：0
作者：
El-Gamel M. [1 ]
Mohamed O. [1 ]
机构：
[1] Department of Mathematical Sciences, Faculty of Engineering, Mansoura University, Mansoura
来源：
SeMA Journal | 2022年 / 79卷 / 2期
关键词：
Chebyshev polynomial; Collocation; Matrix operation; Nonlinear;
D O I：
10.1007/s40324-021-00258-x
中图分类号：
学科分类号：
摘要：
A large class of physical phenomena in biophysics, chemical engineering, and physical sciences are modeled as systems of Fredhold integro-differential equations. In its simplest form, such systems are linear and analytic solutions might be obtained in some cases while numerical methods can be also used to solve such systems when analytic solutions are not possible. For more realistic and accurate study of underlying physical behavior, including nonlinear actions is useful. In this paper, we use the Chebyshev pseudo-spectral method to solve the pattern nonlinear second order systems of Fredholm integro-differential equations. The method reduces the operators to a nonlinear system of equations that can be solved alliteratively. The method is tested against the reproducing kernel Hilbert space (RKHS) method and shows good performance. The present method is easy to implement and yields very good accuracy for using a relatively small number of collocation points. © 2021, The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada.
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页码：383 / 396
页数：13
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共 44 条
  • [1] Al-Smadi M., Abu Arqub O., Shawagfeh N., Momani S., Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method, Appl. Math. Model., 291, pp. 137-148, (2016)
  • [2] Abu Arqub O., Abo-Hammour Z., Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm, Appl. Math. Inf. Sci., 279, pp. 396-415, (2014)
  • [3] Akyuz-Dascioglu A., A Chebyshev polynomial approach for linear Fredholm-Volterra integro-differential equations in the most general form, Appl. Math. Comput., 181, pp. 103-112, (2006)
  • [4] Akyuz-Dascioglu A., cerdik-Yaslan H., The solution of high-order nonlinear ordinary differential equations by Chebyshev Series, Appl. Math. Comput., 12, pp. 5658-5666, (2011)
  • [5] Azodi H., Euler polynomials approach to the system of nonlinear fractional differential equations, J. Math., 51, pp. 71-87, (2019)
  • [6] Baccouch M., Kaddeche S., Efficient Chebyshev pseudospectral methods for Viscous Burgers equations in one and two space dimensions, Int. J. Appl. Comput. Math., 2019, (2019)
  • [7] Bermejo R., Sastre P., An implicit-explicit Runge-Kutta-Chebyshev finite element method for the nonlinear Lithium-ion battery equations, Appl. Math. Comput., 361, pp. 398-420, (2019)
  • [8] Bai A.Z., Gu A.Y., Fan C., A direct Chebyshev collocation method for the numerical solutions of three-dimensional Helmholtz-type equations, Eng. Anal. Bound. Elem., 104, pp. 26-33, (2019)
  • [9] Bakodah H., Al-Mazmumy M., Almuhalbedi S., Solving system of integro differential equations using discrete adomain decomposition method, J. Taibah Univer. Sci., 13, pp. 805-812, (2019)
  • [10] Babolian E., Mordad M., A numerical method for solving systems of linear and nonlinear integral equations of the second kind by hat basis functions, Comput. Math. Appl., 62, pp. 187-198, (2011)
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