This paper proposes the Adams Bash forth two-step method and frequency domain space parallel attention UNet-style architecture (AB2-FSA-UNet-style architecture) model for medical imaging semantic segmentation of skin melanoma. This model combines the Adams Bash forth two-step discretization neural memory ordinary differential equation (nmODE) decoder, channel level contextual anchor attention (CCAA) module, and frequency-domain spatial parallel attention-guided strategy. Introduce CCAA module in the feature representation subnetwork section, use NMODE in the feature reconstruction subnetwork section, and combine frequency domain spatial parallel attention-guided strategy to improve segmentation classification precision and reduce computational complexity. The empirical findings indicate that AB2-FSA-UNet-style architecture has achieved excellent performance on three common datasets: PH2, ISIC2016, and ISIC2017. Compared with methods such as UNet-style architecture model, EGE UNet, FEDUKD, FocalUnetR, DCSAUNet, and FatNet, AB2-FSA-UNet-style architecture has significantly improved classification precision, recall, specificity, F1 index, and IoU index. At the same time, the parameters and computation of this model are relatively low, providing an efficient solution for mobile medical devices and edge computing scenarios. The AB2-FSA-UNet-style architecture model significantly improves the classification precision and efficiency of skin melanoma segmentation by combining the Adam Bash forth two-step discretization nmODE decoder, CCAA module, and frequency-domain spatial parallel attention-guided strategy.