A reduced Galerkin finite element formulation based on proper orthogonal decomposition for the generalized KDV-RLW-Rosenau equation. (English) Zbl 1532.65085
Summary: 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.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Keywords:
generalized KDV-RLW-Rosenau equation; proper orthogonal decomposition; quadratic B-spline Galerkin finite element method; Crank-Nicolson method; error estimatesReferences:
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