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Effective numerical methods for nonlinear singular two-point boundary value Fredholm integro-differential equations | ||
Iranian Journal of Numerical Analysis and Optimization | ||
مقاله 5، دوره 13، شماره 3 - شماره پیاپی 26، آذر 2023، صفحه 444-459 اصل مقاله (366.26 K) | ||
نوع مقاله: Research Article | ||
شناسه دیجیتال (DOI): 10.22067/ijnao.2023.80420.1211 | ||
نویسنده | ||
S. Amiri* | ||
Department of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, P.O. Box: 13846-63113, Tehran, Iran. | ||
چکیده | ||
We deal with some effective numerical methods for solving a class of nonlinear singular two-point boundary value Fredholm integro-differential equations. Using an appropriate interpolation and a q-order quadrature rule of integration, the original problem will be approximated by the non-linear finite difference equations and so reduced to a nonlinear algebraic system that can be simply implemented. The convergence properties of the proposed method are discussed, and it is proved that its convergence order will be of O(hmin{ 72 ,q− 12 }). Ample numerical results are addressed to con- firm the expected convergence order as well as the accuracy and efficiency of the proposed method. | ||
کلیدواژهها | ||
Nonlinear Fredholm integro-differential equations؛ Singular two-point boundary value؛ Numerical method | ||
مراجع | ||
[1] Amiraliyev, G.M., Durmaz, M.E. and Kudu, M. A numerical method for a second order singularly perturbed Fredholm integro-differential equa-tion, Miskolc Math. Notes 22(1) (2021) 37–48. [2] Chambre, P.L. On the solution of the Poisson-Boltzmann equation with application to the theory of thermal explosions, J. Chem. Phys. 20 (1952) 1795–1797. [3] Chandrasekhar, S. Introduction to the Study of Stellar Structure, Dover, New York, 1967. [4] Chen, J., He, M.F. and Huang, Y. A fast multiscale Galerkin method for solving second order linear fredholm integro-differential equation with Dirichlet boundary conditions, J. Comput. Appl. Math. 364 (2020) 112352. [5] Duggan, R.C. and Goodman, A.M. Pointwise bounds for a nonlinear heat conduction model of the human head, Bull. Math. Biol. 48 (2) (1986) 229–236. [6] Durmaz, M.E. and Amiraliyev, G.M. A robust numerical method for a singularly perturbed Fredholm integro-differential equation, Mediterr. J. Math. 18(1) (2021), Paper No. 24, 17 pp. [7] Durmaz, M.E., Amiraliyev, G.M. and Kudu, M. Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition, Turk. J. Math. 46 (1) (2022) 207–224. [8] Durmaz, M.E., Cakır, M. and Amirali, G. Parameter uniform second-order numerical approximation for the integro-differential equations in-volving boundary layers, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 71(4) (2022) 954–967. [9] Flagg, R.C., Luning, C.D. and Perry, W.L. Implementation of new it-erative techniques for solutions of Thomas-Fermi and Emden-Fowler equations, J. Comput. Phys. 38 (3) (1980) 396–405. [10] Gebeyehu, M., Garoma, H. and Deressa, A. Fitted numerical method for singularly perturbed semilinear three-point boundary value problem, Iranian Journal of Numerical Analysis and Optimization, 12(1) (2022)145–162. [11] Gümgüm, S. Taylor wavelet solution of linear and nonlinear Lane-Emden equations, Appl. Numer. Math. 158 (2020) 44–53. [12] Khan, H. and Xu, H. Series solution to the Thomas-Fermi equation, Phys. Lett. A 365 (2007) 111–115. [13] Khan, S. and Khan, A. A fourth-order method for solving singularly perturbed boundary value problems using nonpolynomial splines, Iranian Journal of Numerical Analysis and Optimization, 12 (2) (2022) 483–497. [14] Khuri, S.A. and Sayfy, A. A novel approach for the solution of a class of singular boundary value problems arising in physiology, Math. Comput. Model 52 (3) (2010) 626–636. [15] Kilicman, A., Hashim, I., Tavassoli Kajani, M. and Maleki, M. On the rational second kind Chebyshev pseudospectral method for the solution of the Thomas-Fermi equation over an infinite interval, J. Comput. Appl. Math. 257 (7) (2014) 79–85. [16] Kumar, M., Mishra, H.K. and Singh, P. A boundary value approach for a class of linear singularly perturbed boundary value problems, Adv. Eng. Softw. 10 (2009) 298–304. [17] Lima, P.M. and Morgado, L. Numerical modeling of oxygen diffusion in cells with Michaelis-Menten uptake kinetics, J. Math. Chem. 48 (2010) 145–158. [18] Lin, S.H. Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics, J. Theor. Biol. 60 (2) (1976) 449–457. [19] Mohapatra, J. and Govindarao, L. A fourth-order optimal numerical approximation and its convergence for singularly perturbed time delayed parabolic problems, Iranian Journal of Numerical Analysis and Optimiza-tion, 12 (2) (2022) 250–276. [20] Priyadarshana, S., Sahu, S.R. and Mohapatra, J. Asymptotic and nu-merical methods for solving singularly perturbed differential difference equations with mixed shifts, Iranian Journal of Numerical Analysis and Optimization, 12 (1) (2022) 55–72. [21] Reddy, Y.N. and Chakravarthy, P.P. An initial-value approach for solving singularly perturbed two-point boundary value problems, Appl. Math. Comput. 155 (2004) 95–110. [22] Singh, O.P., Pandey, R.K. and Singh, V.K. An analytic algorithm of Lane-Emden type equations arising in astrophysics using modified Homo-topy analysis method, Comput. Phys. Commun. 180 (2009) 1116–1124. [23] Woldaregay, M.M. and Duressa, G.F. Exponentially fitted tension spline method for singularly perturbed differential difference equations, Iranian Journal of Numerical Analysis and Optimization, 11 (2) (2021) 261–282. [24] Zhang, F. Matrix theory, Springer, New York, 2011. | ||
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