In the paper, a fully discrete compact difference scheme with $O(\tau^{2}+h^{4})$ precision is established by considering the numerical approximation of the one-dimensional Allen-Cahn equation. The numerical solutions satisfy discrete maximum principle under reasonable step ratio and time step constraint is proved. And the energy stability for the fully discrete scheme is investigated. An example is finally presented to show the effectiveness of scheme.

With the increasing demand for security surveillance, assisted driving, and remote sensing, target detection networks with rich environmental perception capabilities and high detection accuracy have become a research hotspot. However, detection techniques based on single-modality images face limitations in environmental adaptability, as they are easily affected by lighting conditions, as well as obstacles such as smoke, rain, and vegetation, leading to information loss and failing to meet the required accuracy. To address these issues, we propose a target detection network—IV-YOLO, which integrates features from both visible and infrared images. We built a dual-branch fusion network based on YOLOv8 (You Only Look Once v8) that combines infrared and visible images for target detection. On this foundation, we designed a Bidirectional Pyramid Feature Fusion structure (Bi-Fusion) to fully integrate complementary features from different modalities, reducing detection errors caused by feature redundancy and extracting fine-grained features of small targets through dual-modal fusion. Additionally, we developed the Shuffle-SPP structure, which combines channel and spatial attention mechanisms to enhance focus on deep features and further aggregate upsampling, extracting richer features. To improve the model’s expressive power, we designed a loss function tailored for multi-scale target detection boxes, accelerating the network’s convergence during training. Experimental results show that the proposed IV-YOLO network achieves an average precision (mAP) of 74.6% on the UAV remote sensing dataset, 75.4% on the KAIST pedestrian dataset, and 84.8% on the FLIR dataset. While ensuring detection accuracy, our model significantly reduces computational load, making it well-suited to meet real-time requirements. This architecture is expected to find broad application in fields such as autonomous driving, public safety, and others.