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

• Published in: Journal of computational and applied mathematics Vol. 308; pp. 435 - 446
• Main Authors: Gouyandeh, Z., Allahviranloo, T., Armand, A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.12.2016
• Subjects: Approximation; Computation; Convergence; Integral equations; Mathematical analysis; Mathematical models; Matrix representation; Nonlinear Volterra–Fredholm–Hammerstein integral equations; Nonlinearity; Sobolev space; Spectra; Tau-collocation method; Nonlinear Volterra–Fredholm–Hammerstein integral equations; Matrix representation; Tau-collocation method; Sobolev space
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2016.06.028

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.