In order to efficiently retrieve the same or similar fabric samples, a fabric image retrieval model based on deep hashing was proposed. The model was improved on the basis of MobileNetV1, and the performance of the model was improved by combining the h-swish activation function and attention mechanism module. The hashing method was used to solve the problem of low feature matching speed caused by high-dimensional feature output. By combining the label information and similarity information of the images, a new loss function was constructed, which solved the problem of low model accuracy caused by the large feature difference between similar samples and the small feature difference between heterogeneous samples in fabric images. The experimental results on self-built fabric image dataset showed that the feature extraction time of the proposed algorithm was 0.25 ms, and the MAP reached 93.2\(\%\), which can take into account the fabric retrieval speed and improve retrieval accuracy at the same time. As a result, it has certain application prospects.

A numerical investigation is conducted for the initial boundary value problem of the Korteweg–de Vries (KdV) equation with homogeneous boundary conditions. Using the average implicit difference discretization, a second-order theoretical accuracy in time is achieved. For the spatial direction, a center-symmetric discretization coupled with the extrapolation technique is employed, yielding a three-level linear difference method with sixth-order accuracy. Consequently, the integration of these methods results in a linear finite difference scheme that accurately simulates the two conserved quantities of the original problem. Furthermore, theoretical results, including the convergence and stability of the proposed scheme, are proved using the discrete Sobolev inequality and the discrete Gronwall inequality. Numerical experiments validate the reliability of the scheme.