A reduced Galerkin finite element formulation based on proper orthogonal decomposition for the generalized KDV-RLW-Rosenau equation

This paper investigates reduced-order modeling of the Korteweg de Vries regularized long-wave Rosenau (KdV-RLW-Rosenau) equation using semi- and fully-discrete B-spline Galerkin approximations. The approach involves the application of a proper orthogonal decomposition (POD) method to a Galerkin finite element (GFE) formulation, resulting in a POD GFE formulation with lower dimensions and high accuracy. The error between the reduced POD GFE solution and the traditional GFE solution is analyzed using the Crank-Nicolson method. Numerical examples show that the theoretical conclusions are consistent with the results of the numerical computation, and that the POD method is effective and feasible.