Numerical-analytic method of solving two-point problems for systems of partial integrodifferential equations (Q1176874)

A generalized Samoilenko-Ronto method is considered to prove the existence and uniqueness of the solution \(u(t,x)\) of the system of integro-differential equations \(u_{xt}=F(t,x,Du,G(Du))\) with initial and two-point boundary conditions. Basic assumptions are: continuity of \(u\) and the differential operator \(Du\), Lipschitz condition for the integral operator \(G\) and for the general operator \(F\). The solution \(u\) is constructed by Picard iteration.