×

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.

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45G10 Other nonlinear integral equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Brunner, H., Collocation Method for Volterra Integral and Related Functional Equations (2004), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1059.65122
[2] Delves, L. M.; Mohamed, J. L., Computational Methods for Integral Equations (1985), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0592.65093
[3] Burton, T. A., Volterra Integral and Differential Equations (2005), Elsevier B.V.: Elsevier B.V. Netherlands · Zbl 1075.45001
[4] Chihara, T. S., An Introduction to Orthogonal Polynomials (1978), Gordon & Breach, Science Publisher Inc.: Gordon & Breach, Science Publisher Inc. New York · 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, 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, 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)
[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
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.