数学
数学分析
趋同(经济学)
领域(数学)
非线性系统
正多边形
能量(信号处理)
有限差分法
功能(生物学)
能量泛函
相(物质)
有限差分
应用数学
几何学
纯数学
物理
量子力学
进化生物学
经济
生物
经济增长
统计
作者
Steven M. Wise,C. Wang,John Lowengrub
摘要
We present an unconditionally energy stable finite-difference scheme for the phase field crystal equation. The method is based on a convex splitting of a discrete energy and is semi-implicit. The equation at the implicit time level is nonlinear but represents the gradient of a strictly convex function and is thus uniquely solvable, regardless of time step size. We present local-in-time error estimates that ensure the convergence of the scheme. While this paper is primarily concerned with the phase field crystal equation, most of the theoretical results hold for the related Swift–Hohenberg equation as well.
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