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

TL;DR

This paper introduces a monotone domain decomposition iterative method for nonlinear Volterra-type integro-differential equations, proving its convergence and establishing existence and uniqueness of solutions.

Contribution

It develops a new iterative scheme that ensures convergence for nonlinear Volterra equations by modifying the original equation to achieve monotonicity.

Findings

Proved convergence of the iterative method.

Established existence and uniqueness of solutions.

Demonstrated effectiveness for nonlinear Volterra equations.

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.