👉 Wavelet Variational Methods (WVMs) are a class of mathematical techniques that combine the principles of wavelet analysis with variational calculus to solve partial differential equations (PDEs) and other mathematical problems. These methods represent functions as a sum of wavelets, which are localized functions that can capture both frequency and spatial information. By formulating the problem in a variational framework, WVMs derive an optimization problem that minimizes a functional, often related to the energy of the solution. This approach allows for efficient and accurate approximations, particularly useful in problems with complex geometries or discontinuities, where traditional methods might struggle. WVMs are widely applied in signal processing, image analysis, and physics for tasks like denoising, compression, and solving PDEs.
