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Hybrid Function Method for Solving Nonlinear Fredholm Integral Equations of the Second Kind

Authors: jianhua Hou, Changqing Yang, and Beibo Qin

Abstract:

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function  approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

Keywords: Fredholm Integral Equation, Chebyshev polynomials, Hybrid functions, Blockpulse, product operational matrix

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1087876

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References:


[1] F.Bloom, Asymptotic bounds for solutions to a system of damped integrodifferential equations of electromagnetic theory, J. Math. Anal. Appl. 73(2) (1980), 524-542.
[2] K. Holmaker, Global asymptotic stability for stationary solution of system of integro-differential equations describing the formation of liver zones, SIAM J. Math. Anal. 24(1) (1993), 116-128.
[3] J. Frankel, A Galerkin solution to regularized Cauchy singular integrodifferential equations, Quart. Appl. Math. 52 (2) (1995), 145-258.
[4] K. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge, England: Cambridge University Press, 1997.
[5] L.M. Delves, A fast method for the solution of Fredholm integral equations, IMA.J. Appl. Math. 20 (2) (1977), 173-182.
[6] L.M. Delves, J.L. Mohamed, Computational Methods for Integral Equations, Cambridge, England: Cambridge University Press, 1988.
[7] L.M. Delves, J. Walsh, Numerical Solution of Integral Equations, Oxford, England: Oxford Univ. Press, 1974.
[8] K. Atkinson , H. Weimin, Theoretical Numerical Analysis, A Functional Analysis Framework, 3rd ed. New York, USA: Springer, 2009.
[9] C. Yang, J. Hou ang B. Qin Numerical solution of Riccati differential equations by using hybrid functions and tau method, International Journal of mathematical and Comutational Sciences 6(2012) 205-208.
[10] M. Razzaghi, H.R. Marzban, Direct method for variational problems via hybrid of Block-pulse and Chebyshev functions, Math. Probl. Eng. 6 (2000), 85-97.
[11] C. Canuto, M.Y. Hussaini, A.Quarteroni, T. A. Zang, Spectral Methods on Fluid Dynamics, Annu. Rev. Fluid. Mech. 19(1)(1987)339-367.
[12] M.T. Kajani, A.H. Vencheh, Solving second kind integral equations with Hybrid Chebyshev and Block-Pulse functions, App.Math.Comput. 163(2005), 71-77.
[13] E. Babolian, A. Shahsavaran, Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets, J. Comput. Appl. Math. 25(2009),87-95.