AN APPLICATION OF BANACH’S CONTRACTIONPRINCIPLE TO THE NUMERICAL TREATMENT OFNONLINEAR VOLTERRA-FREDHOLM EQUATIONS INHEALTH DOMAINS

Abstract

This paper investigates the numerical approximations of nonlinear
Volterra-Fredholm equations, focusing on their bounded solutions over specified regions. The research employed the Banach contraction principle to prove the existence of a unique solution in the space of continuous functions. The integral equations were formulated to model complex interactions in various applications, particularly infectious disease dynamics. Also, some key paramters, like the kernel functions and scalar multipliers were analyzed to ascertain that the contraction mappings conditions are satisfied. The Picard iteration was used to approximate solutions, proving convergence and stability results.
The findings showed significance of these mathematical models in dynamic
systems and optimizing treatment in healthcare. This work contributes to the existing literature on nonlinear integral equations.