Monotone Domain Decomposition Iterative Method and its Convergence for a Nonlinear Integro-Differential Equation of Volterra Type

Abstract

We apply the monotone domain decomposition iterative method to a nonlinear integro-differential equation of Volterra type and prove its convergence. To do this, by adding a term in both sides of the original equation we make a linear equation to get a monotone domain decomposition iterative scheme and prove the existence, uniqueness and convergence of iterative solutions.