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Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polynomials. (English) Zbl 1114.65370
Summary: Orthogonal Chebyshev polynomials are developed to approximate the solutions of linear and nonlinear Volterra integral equations. Properties of these polynomials and some operational matrices are first presented. These properties are then used to reduce the integral equations to a system of linear or nonlinear algebraic equations. Numerical examples illustrate the pertinent features of the method.

65R20Integral equations (numerical methods)
45D05Volterra integral equations
45G10Nonsingular nonlinear integral equations
Full Text: DOI
[1] Brunner, H.: Collocation method for Volterra integral and related functional equations. (2004) · Zbl 1059.65122
[2] Delves, L. M.; Mohamed, J. L.: Computational methods for integral equations. (1985) · Zbl 0592.65093
[3] Burton, T. A.: Volterra integral and differential equations. (2005) · Zbl 1075.45001
[4] Chihara, T. S.: An introduction to orthogonal polynomials. (1978) · Zbl 0389.33008
[5] Maleknejad, K.; Kajani, M. T.; Mahmoudi, Y.: Numerical solution of Fredholm and Volterra integral equation of the second kind by using Legendre wavelets. Kybernetes 32, No. 9 -- 10, 1530-1539 (2003) · Zbl 1059.65127
[6] Maleknejad, K.; Aghazadeh, N.: Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method. Appl. math. Comput. 161, 915-922 (2005) · Zbl 1061.65145
[7] Sezer, M.: Taylor polynomial solution of Volterra integral equations. Int. J. Math. edu. Sci. technol. 25, No. 5, 625 (1994) · Zbl 0823.45005
[8] Yalsinbas, S.: Taylor polynomial solutions of nonlinear Volterra -- Fredholm integral equations. Appl. math. Comput. 127, 195-206 (2002) · Zbl 1025.45003
[9] Rashed, M. T.: Lagrange interpolation to compute the numerical solutions of differential, integral and integro-differential equations. Appl. math. Comput. 151, 869-878 (2004) · Zbl 1048.65133