Convergence of solutions for functional integro-differential equations with nonlinear boundary conditions

Abstract

Abstract This paper is concerned with the convergence of solutions for a class of functional integro-differential equations with nonlinear boundary conditions. New comparison principles are obtained. By using the comparison principles and quasilinearization method, we present two monotone iterative sequences uniformly and monotonically converging to the unique solution with rate of order 2. Meanwhile, an example is given to demonstrate applications of the result reported.

Keywords

• Functional integro-differential equations
• Monotone iterative
• Quasilinearization
• Nonlinear boundary conditions
• Coupled lower and upper solutions