Yang, Changqing Chebyshev polynomial solution of nonlinear integral equations. (English) Zbl 1278.65206 J. Franklin Inst. 349, No. 3, 947-956 (2012). Summary: The Chebyshev collocation method is adopted to find an approximate solution for nonlinear integral equations. Properties of the Chebyshev polynomials and the operational matrix are used in the integral equation of a system consisting of nonlinear algebraic equations with the unknown Chebyshev coefficients. Numerical examples are presented to illustrate the method and results are discussed. Cited in 7 Documents MSC: 65R20 Numerical methods for integral equations 45B05 Fredholm integral equations 45D05 Volterra integral equations 45G10 Other nonlinear integral equations Keywords:Fredholm integral equation; Volterra integral equation; Chebyshev collocation method; nonlinear integral equations; numerical examples PDFBibTeX XMLCite \textit{C. Yang}, J. Franklin Inst. 349, No. 3, 947--956 (2012; Zbl 1278.65206) Full Text: DOI Link References: [1] Burton, T. A., Volterra Integral and Differential Equations (2005), Elsevier B.V.: Elsevier B.V. Netherlands · Zbl 1075.45001 [2] Yashilbas, S., Taylor polynomial solution of nonlinear Volterra-Fredholm integral equations, Applied Mathematics and Computing, 127, 195-206 (2002) [3] Yousefi, S.; Razzaghi, M., Legendre Wavelet method for the nonlinear Volterra-Fredholm integral equations, Mathematics and Computers in Simulation, 70, 1-8 (2005) · Zbl 1205.65342 [4] Malekneajad, K.; Kajani, M. T.; Mahmoudi, Y., Numerical solution of linear Fredholm and Volterra integral equation of the second kind using Legendre wavelets, Kybernetes, 32, 9-10, 1530-1539 (2003) · Zbl 1059.65127 [5] Nurcan, Kurt; Mehmet, Sezer, Polynomial solution of high-order linear Fredholm integro-differential equations with constant coefficients, Journal of the Franklin Institute, 345, 839-850 (2008) · Zbl 1202.65172 [6] Maleknejad, K.; Sohrabi, S., Numerical solution of nonlinear Volterra integral equations of the second kind using Chebyshev polynomials, Applied Mathematics and Computing, 188, 123-128 (2007) · Zbl 1114.65370 [7] Yusufoğlu (Agadjanov), E., Numerical solving initial value problem for Fredholm type linear integro-differential equation system, Journal of the Franklin Institute, 346, 636-649 (2009) · Zbl 1168.45300 [8] Ghasemi, M.; Tavassoli, M.; Bobolian, E., Numerical solutions of the Volterra-Fredholm integral equations using homotopy perturbation method, Applied Mathematics and Computing, 188, 446-449 (2007) · Zbl 1114.65367 [9] Sloss, B. G.; Blyth, W. F., A Walsh function method for a non-linear Volterra integral equation, Journal of the Franklin Institute, 340, 25-41 (2003) · Zbl 1023.65141 [10] Babolian, E.; Davari, A., Numerical implementation of Adomian decomposition method, Applied Mathematics and Computing, 153, 301-305 (2004) · Zbl 1048.65131 [11] Canuto, C.; Hussaini, M. Y.; Quarteroni, A.; Zhang, T. A., Spectral Methods on Fluid Dynamics (1988), Springer-Verlag: Springer-Verlag NY, USA [12] Delves, L. M.; Mohamed, J. L., Computational Methods for Integral Equations (1985), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0592.65093 [13] Sag, T. W., Chebyshev iteration methods for integral equations of the second kind, Mathematics of Computation, 24, 110, 314-355 (1970) · Zbl 0218.65036 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.