On a symptotic methods for Fredholm–Volterra integral equation of the second kind in contact problems

摘要

A method is used to obtain the general solution of Fredholm–Volterra integral equation of the second kind in the space L2(Ω)×C(0,T),0⩽t⩽T<∞;Ω is the domain of integrations.The kernel of the Fredholm integral term belong to C([Ω]×[Ω]) and has a singular term and a smooth term. The kernel of Volterra integral term is a positive continuous in the class C(0,T), while Ω is the domain of integration with respect to the Fredholm integral term.Besides the separation method, the method of orthogonal polynomials has been used to obtain the solution of the Fredholm integral equation. The principal (singular) part of the kernel which corresponds to the selected domain of parameter variation is isolated. The unknown and known functions are expanded in a Chebyshev polynomial and an infinite algebraic system is obtained.