Quantum computing relies on the accurate modeling of some fundamental components, many of which are based on superconducting technologies. Among these, Josephson junctions are of particular importance, as they play a crucial role in both qubit implementation and auxiliary technologies like parametric amplifiers [1, 2]. Accurately simulating such superconducting devices is a key challenge in computational physics, particularly in the study of quantum technologies. These amplifiers are essential for high-fidelity qubit readout and control, but their mathematical modeling involves nonlinear differential equations with highly oscillatory solutions, which standard numerical methods struggle to solve efficiently, since a very small stepsize is required to obtain the prescribed accuracy. This work introduces a computational technique based on exponential fitting theory [3] to address these difficulties. The proposed method adopts a predictor-corrector structure and incorporates prior knowledge of system characteristics, such as oscillation frequency and damping factors, to construct a suitable functional basis for numerical discretization. Numerical tests on highly oscillatory scenarios confirm the method’s effectiveness in capturing the intricate dynamics of Josephson junctions at a reasonable computational cost. The approach provides a valuable tool for improving the numerical modeling of superconducting circuits, contributing to the broader effort of refining simulation techniques in quantum computing. REFERENCES [1] N. D. Mermin, Quantum Computer Science: An Introduction, Cambridge University Press, 2007. [2] C. Guarcello, C. Barone, G. Carapella, V. Granata, G. Filatrella, A. Giachero, S. Pagano, Driving a Josephson Traveling Wave Parametric Amplifier into chaos: Effects of a non-sinusoidal current–phase relation, Chaos, Solitons & Fractals, 189, 2024. [3] L. Gr. Ixaru, Exponential Fitting, Kluwer Academic Publishers, 2004.