Toeplitz matrix method and nonlinear integral equation of Hammerstein type

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摘要

The existence and uniqueness solution of the nonlinear integral equation of Hammerstein type with discontinuous kernel are discussed. The normality and continuity of the integral operator are proved. Toeplitz matrix method is used, as a numerical method, to obtain a nonlinear system of algebraic equations. Also, many important theorems related to the existence and uniqueness of the produced algebraic system are derived. Finally, numerical examples, when the kernel takes a logarithmic and Carleman forms, are discussed and the estimate error, in each case, is calculated.

论文关键词:45 B 05,45 G 10,65 R,Nonlinear integral equation,Hammerstein type,Toeplitz matrix method,Nonlinear algebraic system

论文评审过程:Received 4 January 2007, Revised 15 February 2008, Available online 26 February 2008.

论文官网地址:https://doi.org/10.1016/j.cam.2008.02.012