On the solution of linear and nonlinear integral equation

摘要

The purpose of this paper is to establish the solution of Fredholm–Volterra integral equation of the second kind in the space L2(Ω)×C[0,T] considering the following when, Fredholm integral term in Li2(Ω) and Volterra integral term, in [0,T], are linear. Also, each of Fredholm or Volterra integral term is linear while the other term is nonlinear.Here, Ω is defined as the domain of integration with respect to position, while t is consider as the time, t∈[0,T], T<∞. Also the Fredholm–Volterra integral equation of the first kind is established as special case of these work. Many special in one, two and three dimensional problems of integral equation are considered. Representing the kernel of Fredholm integral term, in the form of logarithmic function, Carleman function, potential and generalized potential function and Macdonald function are considered.