Applying faster algorithm for obtaining convergence, stability, and data dependence results with application to functional-integral equations

Abstract

The goal of this manuscript is to create a new faster iterative algorithm than the previous writing's sober algorithms. In the setting of Banach spaces, this algorithm is used to analyze convergence, stability, and data-dependence results. Basic numerical examples are also provided to highlight the behavior and effectiveness of our approach. Ultimately, the proposed approach is used to solve the functional Volterra-Fredholm integral problem as an application.

Keywords

• convergence result
• fixed point
• data-dependent result
• ξ-stable
• numerical experiment
• functional integral equation