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

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• 作者：Z. Gouyandeh^a ; ^{Zgouyandeh@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; T. Allahviranloo^b ; ^{Tofigh@allahviranloo.com" class="auth_mail" title="E-mail the corresponding author} ; A. Armand^c ; ^{Atefeh.armand@ymail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Tau-collocation method ; Nonlinear Volterra&ndash ; Fredholm&ndash ; Hammerstein integral equations ; Matrix representation ; Sobolev space
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 December 2016
• 年：2016
• 卷：308
• 期：Complete
• 页码：435-446
• 全文大小：514 K

文摘

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${}^2$-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.