Monotone methods for periodic solutions of second order scalar functional differential equations (Q792071)

The paper describes an iterative method which starting from a lower or from an upper periodic solution, provides a monotone sequence converging to a periodic solution of the second order scalar differential equation \(u''=f(t,u,u'),\quad \quad a\leq t\leq b\) with periodic boundary conditions \(u(a)-u(b)=0,\quad \quad u'(a)-u'(b)=0.\) Under suitable restrictions on the growth of f the method extends to the periodic solutions of functional differential equations of type \[ x''=f(t,x(t),x(g(t)),x'(t),x'(h(t))) \] where f is periodic with respect to t. The paper also gives the convergence, rate of convergence and two numerical examples with an a posteriori error analysis of the iterative method.