Quasi-Spectral Method for Nonlinear Partial Differential KdV Equation in Image Processing

Abstract

Image processing method based on nonlinear partial differential equations not only has better accuracy than the linear processing method, but also can deal with some of the image gradient, geometric features such as curvature. Therefore, this paper studies the numerical solution of nonlinear partial differential equation KdV equation. To solve the problem of low calculation accuracy of finite element method, finite difference method and Galerkin method, a high precision solution of KdV equation is realized by using Fourier expansion based on Quasi-spectral method in this paper. And the high precision of this method is verified by numerical experiment.