Jacobi and Gauss-Seidel iterative methods to find solutions for systems of equations. Parameters: - A: 2D numpy array, the coefficient matrix. - b: 2D numpy array, the independent vector. - x0: 2D ...

In this paper, based on classical Lie group method, we study multi-dimensional Landau-Lifshitz equation, and get its infinitesimal generator, symmetry group and new solutions. In particular, we build ...

Nonlinear problems, originating from applied science that is closely related to practices, contain rich and extensive content. It makes the corresponding nonlinear models also complex and diverse. Due ...

Elliptic systems, comprising sets of partial differential equations marked by elliptic operators, are central to understanding equilibrium states in many physical and biological contexts. In ...