The present paper proposes a new monotone iteration principle for the existence as well as approximations
of the tripled solutions for a tripled periodic boundary value problem of second order ordinary nonlinear
differential equations. An algorithm for the tripled solutions is developed and it is shown that the sequences
of successive approximations defined in a certain way converge monotonically to the tripled solutions of the
related differential equations under some suitable hybrid conditions. A numerical example is also indicated
to illustrate the abstract theory developed in the paper.