Reduction of an infinite system of integrodifferential equations for electric currents on a lattice of closed curves to a finite system of independent pseudodifferential equations on a circle (Q1914812)

Under the conditions of periodicity and nonresonance, it is shown that the infinite system of integro-differential equations on an infinite network of nonintersecting infinitely smooth simple closed curves in the plane can be reduced to a finite system of independent pseudodifferential equations on the unit circle, and this reduction allows one to apply the many known powerful methods for the numerical analysis of classic elliptic pseudodifferential equations on the unit circle to the original system.