Monotone Iterative Technique for Nonlinear Volterra-Fredholm Integro-Differential Equations

Abstract

This paper presents an efficient algorithm based on a monotone method for the solution of a class of nonlinear Volterra-Fredholm integro-differential equations of second order. This method is applied to derive two monotone sequences of upper and lower solutions which are uniformly convergent. Theoretical analysis of the existence and convergence of those sequences are discussed. The numerical results demonstrate reliability and efficiency of the proposed technique.