Cross-domain few-shot segmentation (CD-FSS) aims to segment unseen categories with very limited samples while alleviating the negative effects of domain shift between the source and target domains. At present, existing CD-FSS studies typically rely on multiple independent modules to enhance cross-domain adaptability. However, the independence among these modules hinders the effective flow of knowledge, making it difficult to fully leverage their collective potential. In contrast, this paper proposes an all-in-one module based on ordinary differential equations (ODEs) and the Fourier transform, resulting in a structurally concise method-Few-Shot Segmentation over Time Intervals (FSS-TIs). FSS-TIs not only explores a domain-agnostic feature space, but also achieves significant performance improvement through target-domain fine-tuning with extremely limited support samples. Specifically, the ODE modeling process incorporates nonlinear transformations and random perturbations of the amplitude and phase spectra, effectively simulating potential target-domain data distributions. Meanwhile, the analytical solution of the ODE is transformed into a theoretically infinitely iterable feature refinement process, thereby enhancing the learning capability under limited support samples. In this way, both the exploration of domain-agnostic features and the few-shot learning problem can be addressed through the optimization of the intrinsic parameters of the ODE. Moreover, during target-domain fine-tuning, we strictly constrain the support samples to match the settings of real-world CD-FSS tasks, without incurring additional annotation costs. Experimental results demonstrate the superiority of FSS-TIs over existing CD-FSS methods, and in-depth ablation studies further validate the cross-domain adaptability of FSS-TIs.