Catastrophic overfitting (CO) poses a significant challenge to fast adversarial training (FastAT), particularly at large perturbation scales, leading to dramatic reductions in adversarial test accuracy. Our analysis of existing FastAT methods shows that CO is accompanied by abrupt and irregular fluctuations in loss convergence, indicating that a stable training dynamic is key to preventing CO. Therefore, we propose a training model that uses the Douglas-Rachford (DR) splitting technique to ensure a balanced and consistent training progression, effectively counteracting CO. The DR splitting technique, known for its ability to solve complex optimization problems, offering a distinct advantage over classical FastAT methods by providing a smoother loss convergence. This is achieved without resorting to complex regularization or incurring the computational costs associated with double backpropagation, presenting an efficient solution to enhance adversarial robustness. Our comprehensive evaluation conducted across standard datasets, demonstrates that our DR splitting-based model not only improves adversarial robustness but also achieves this with remarkable efficiency compared to various FastAT methods. This efficiency is particularly observed under conditions involving long training schedules and large adversarial perturbations.