The product Nystr–m method and Volterra-Hammerstien Integral Equation with A Generalized Singular Kernel

Abstract

In this work, the existence of a unique solution of Volterra-Hammerstein integral equation of the second kind (V-HIESK) is discussed. The Volterra integral term (VIT) is considered in time with a continuous kernel, while the Fredholm integral term (FIT) is considered in position with a generalized singular kernel. Using a numerical technique, V-HIESK is reduced to a nonlinear system of Fredholm integral equations (SFIEs). Using product Nystrom method we have a nonlinear algebraic system of equations. Finally, some numerical examples when the kernel takes the logarithmic, and Carleman forms, are considered.