Numerical solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via Tau-collocation method with convergence analysis

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摘要

In this paper, we consider the nonlinear Volterra–Fredholm–Hammerstein integral equations. The approximate solution for the nonlinear Volterra–Fredholm–Hammerstein integral equations is obtained by using the Tau-Collocation method. To do this, the nonlinear Volterra–Fredholm–Hammerstein integral equations is transformed into a system of nonlinear algebraic equations in matrix form. Thus by solving this system unknown coefficients are obtained. The spectral rate of convergence for the proposed method is established in the L2-norm. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the Tau-collocation method is of high accuracy, more convenient and efficient for solving nonlinear Volterra–Fredholm–Hammerstein integral equations.

论文关键词:Tau-collocation method,Nonlinear Volterra–Fredholm–Hammerstein integral equations,Matrix representation,Sobolev space

论文评审过程:Received 19 November 2015, Revised 25 April 2016, Available online 28 June 2016, Version of Record 19 July 2016.

论文官网地址:https://doi.org/10.1016/j.cam.2016.06.028