A composite collocation method for the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations. (English) Zbl 1221.65340

Marzban, H. R.; Tabrizidooz, H. R.; Razzaghi, M.

Commun. Nonlinear Sci. Numer. Simul. 16, No. 3, 1186-1194 (2011).

Summary: This paper presents a computational technique for the solution of the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations. The method is based on the composite collocation method. The properties of hybrid of block-pulse functions and Lagrange polynomials are discussed and utilized to define the composite interpolation operator. The estimates for the errors are given. The composite interpolation operator together with the Gaussian integration formula are then used to transform the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations into a system of nonlinear equations. The efficiency and accuracy of the proposed method is illustrated by four numerical examples.

MSC:

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

Keywords:

mixed Volterra-Fredholm-Hammerstein integral equations; composite collocation method; hybrid functions; block-pulse functions; Lagrange interpolating polynomials; nonlinear integral equations

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