论文标题
一般哈密顿局部微分方程的显式高阶保护方法
Explicit high-order energy-preserving methods for general Hamiltonian partial differential equations
论文作者
论文摘要
对于具有非典型结构矩阵的一般哈密顿局部微分方程，提出了一种新型的显式高阶传播方法。当能量不是二次的时，首先要通过通过能量二次化方法将原始系统重新构成等效形式。然后，通过将显式高阶runge-kutta方法与正交投影技术相结合，使满足二次能源保护定律的最终系统被及时离散。所提出的方案显示出具有显式runge-kutta方法的顺序，因此可以达到所需的高阶精度。此外，这些方法是能量保护和明确的，因为可以明确地解决投影步骤。与其他结构保存方法相比，确定了数值结果以证明所提出的方案的显着优势。
A novel class of explicit high-order energy-preserving methods are proposed for general Hamiltonian partial differential equations with non-canonical structure matrix. When the energy is not quadratic, it is firstly done that the original system is reformulated into an equivalent form with a modified quadratic energy conservation law by the energy quadratization approach. Then the resulting system that satisfies the quadratic energy conservation law is discretized in time by combining explicit high-order Runge-Kutta methods with orthogonal projection techniques. The proposed schemes are shown to share the order of explicit Runge-Kutta method and thus can reach the desired high-order accuracy. Moreover, the methods are energy-preserving and explicit because the projection step can be solved explicitly. Numerical results are addressed to demonstrate the remarkable superiority of the proposed schemes in comparison with other structure-preserving methods.
