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An iterative method for robust solutions to nonlinear Volterra integral equations: Stability, convergence, and practical applications

Isaac Azure

Article ID: 2646
Vol 2, Issue 1, 2024

DOI: https://doi.org/10.54517/mss.v2i1.2646
VIEWS - 42 (Abstract)

Abstract

The paper introduces an iterative method for solving nonlinear Volterra integral equations and analyzes its convergence, stability, and application through examples. It expresses the general nonlinear Volterra integral equation as a series and decomposes the nonlinear operator to derive a recursive formula for the proposed iterative method. The method ensures absolute and uniform convergence, with stability analysis conducted to ensure bounded errors in the presence of perturbations. Convergence analysis utilizes the Lipschitz condition, demonstrating the uniform convergence of the solution series. Illustrative examples, including power nonlinearity and trigonometric functions, validate the stability and convergence of the method. Through graphical representations, convergence analyses for specific integral equations demonstrate the method’s effectiveness and applicability in solving diverse nonlinear integral equations. Overall, the paper contributes a robust iterative method with insights into its stability and convergence properties, supported by practical examples.

Keywords

nonlinear Volterra integral equations; iterative method; convergence analysis; stability analysis; Lipschitz condition; illustrative examples; series representation

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