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

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

Runge-Kutta and Block by Block Methods to Solve Linear Two-Dimensional Volterra Integral Equation with Continuous Kernel

In this paper, the existence and uniqueness of solution of the linear two dimensional Volterra integral equation of the second kind with Continuous Kernel are discussed and proved.RungeKutta method(R. KM)and Block by block method (B by BM) are used to solve this type of two dimensional Volterra integral equation of the second kind. Numerical examples are considered to illustrate the effectiveness of the proposed methods and the error is estimated

Runge-Kutta and Block by Block Methods to Solve Linear Two-Dimensional Volterra Integral Equation with Continuous Kernel

In this paper, the existence and uniqueness of solution of the linear two dimensional Volterra integral equation of the second kind with Continuous Kernel are discussed and proved.RungeKutta method(R. KM)and Block by block method (B by BM) are used to solve this type of two dimensional Volterra integral equation of the second kind. Numerical examples are considered to illustrate the effectiveness of the proposed methods and the error is estimated