Chebyshev spectral solution of nonlinear Volterra-Hammerstein integral equations. (English) Zbl 0873.65122

Using an implicit form of a given Volterra-Hammerstein integral equation introduced for Fredholm-Hammerstein equations by S. Kumar and I. H. Sloan [Math. Comput. 48, 585-593 (1987; Zbl 0616.65142)], and adapted for Volterra-type equations by H. Brunner [Appl. Numer. Math. 9, No. 3-5, 235-247 (1992; Zbl 0761.65103)] the authors approximate its solution by using collocation techniques for a Chebyshev spectral interpolant. The resulting integrals are discretized by employing Chebyshev-Lobatto quadrature formulas. The convergence results are complemented by a numerical illustration.


65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations


Full Text: DOI


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