Monotone iterative sequences for nonlinear integro-differential equations of second order

This paper presents an efficient algorithm based on a monotone method for the solution of a class of nonlinear integro-differential equations of second order. This method is applied to derive two monotone sequences of upper and lower solutions which are uniformly convergent. Theorems which list the conditions for the existence of such sequences are presented. The numerical results demonstrate reliability and efficiency of the proposed algorithm.