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Abstract
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Nonlinear Volterra integro-differential equations are widely used to model complex phenomena in physics, engineering, biology, and control systems, capturing memory effects and nonlinear interactions that cannot be described by ordinary differential equations. However, their nonlinearity and integral components make them difficult to solve accurately and efficiently with traditional numerical methods, which often suffer from instability, ill-conditioning, slow convergence, and high computational cost, particularly for long-time simulations or strongly nonlinear problems. This creates a critical need for robust, high-accuracy numerical techniques capable of handling these challenges. The proposed barycentric rational approach addresses this gap by offering enhanced numerical stability, improved approximation of nonlinear and integral terms, and reduced computational effort, enabling precise and efficient solutions of complex integro-differential models. The importance of this research lies in providing a reliable and versatile computational framework that advances both theoretical understanding and practical applications in areas requiring accurate modeling of nonlinear memory-dependent systems.
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