A Linear Energy-Preserving Finite Volume Element Method for the Improved Korteweg−de Vries Equation

Abstract

In this paper, we introduce a linearized energy-preserving scheme which preserves the discrete global energy of solutions to the improved Korteweg−deVries equation. The method presented is based on the finite volume element method, by resorting to the variational derivative to transform the improved Korteweg−deVries equation into a new form, and then designing energy-preserving schemes for the transformed equation. The proposed scheme is much more efficient than the standard nonlinear scheme and has good stability. To illustrate its efficiency and conservative properties, we also compare it with other nonlinear schemes. Finally, we verify the efficiency and conservative properties through numerical simulations.