Nyström method is a standard numerical technique to solve Fredholm integral equations of the second kind where integration kernel approximated using quadrature formula. Traditionally, rule used classical polynomial Gauss quadrature. Motivated by observation that given function can be better spline lower degree than single piece higher degree, in this work, we investigate use Gaussian rules for ...

In this paper the existence of a positive measurable solution of the Hammerstein equation of the first kind with a singular nonlinear term at the origin is presented. 0. Introduction The literature on the Hammerstein equations with the reciprocal of the solution in the integrand is rather limited, although there are many applications. For example, the equation

It is well known that any classical Lotka–Volterra (LV) operator (associated with quadratic stochastic operator) defined on the simplex a homeomorphism. On other hand, more general LV systems have important applications in time evolution of conflicting species biology. natural to study bijectivity such kind operators. There an example which not injective. In this paper, we introduce class opera...

Abstract: In this work, the operational Tau method is presented to find the solutions of the linear and nonlinear Volterra-Fredholm-Hammerstein integral equations (VFHIEs) of the second kind. Some simple matrices in extension of Tau method for the numerical solutions of VFHIEs is applied. In fact, operational Tau method converts the integral parts of the desired VFHIEs to some operational matri...