Volterra–Fredholm integral equation of the first kind and spectral relationships

摘要

Here, the solution in one, two and three dimensional for the Volterra–Fredholm integral equation of the first kind is obtained in the space L2(Ω)×C[0,T], T<∞. Using a numerical method the integral equation of Volterra–Fredholm becomes a linear system of Fredholm integral equation when that the kernel of Fredholm integral takes a logarithmic form, Carleman function, generalized potential function and Macdonald function are considered as special cases.