  We study equations with infinitely many derivatives. Equations of this type
form a new class of equations in mathematical physics. These equations
originally appeared in p-adic and later in fermionic string theories and their
investigation is of much interest in mathematical physics and applications, in
particular in cosmology. Differential equation with infinite number of
derivatives could be written as nonlinear integral equations. We perform
numerical investigation of solutions of the equations. It is established that
these equations have two different regimes of the solutions: interpolating and
periodic. The critical value of the parameter q separating these regimes is
found to be q^2=1.37. Convergence of iterative procedure for these equations is
proved.
