中文摘要：

能量散逸性是物理和力学中某些微分方程一项重要的物理特性.构造精确地保持微分方程能量散逸性的数值格式对模拟具有能量散逸性的微分方程具有重要的意义.本文利用四阶平均向量场方法和傅里叶谱方法构造了Cahn-Hilliard方程高阶保能量散逸性格式.数值结果表明高阶保能量散逸性格式能很好地模拟Cahn-Hilliard方程在不同初始条件下解的行为,并且很好地保持了Cahn-Hilliard方程的能量散逸特性.

英文摘要：

Energy-dissipating is a very important physical property of some differential equations in physics and mechanics. It has important meaning in simulating the energy dissipating partial differential equation to constructing a numerical scheme which preserves the energy dissipation property of the differential equation precisely. In this paper,we propose a high order energy-dissipating formula of the Cahn-Hilliard equation by the fourth-order average vector field method and Fourier pseudospeetral method. Numerical results show that the high order preserving energy-dissipating formula can well simulate the behavior of the Cahn- Hilliard equation with different initial conditions and preserve the energy-dissipating property of the Cahn-Hilliard equation.