AN APPLICATION OF BANACH’S CONTRACTION PRINCIPLE TO THE NUMERICAL TREATMENT OF NONLINEAR VOLTERRA-FREDHOLM EQUATIONS IN HEALTH DOMAINS

IKENNA STEPHEN OKEKE

IKENNA STEPHEN OKEKE DEPARTMENT OF INDUSTRIAL MATHEMATICS AND HEALTH STATISTICS, DAVID UMAHI FED- ERAL UNIVERSITY OF HEALTH SCIENCES, UBURU, EBONYI STATE, NIGERIA.

Keywords: Banach contraction principle, Nonlinear integral equations, Viral dynamics

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 parameters, 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.

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