| 二维Allen-Cahn方程的有限差分法/配点法求解 |
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| 引用本文： | 邓杨芳,姚泽丰,汪精英,翁智峰.二维Allen-Cahn方程的有限差分法/配点法求解[J].华侨大学学报(自然科学版),2020,41(5):690-694. |
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| 作者姓名： | 邓杨芳 姚泽丰 汪精英 翁智峰 |
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| 作者单位： | 华侨大学 数学科学学院, 福建 泉州 362021 |
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| 基金项目： | 国家自然科学基金;中央高校基本科研业务费专项 |
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| 摘 要： | 对二维Allen-Cahn方程中的时间方向采用有限差分法,空间方向采用重心插值配点法,非线性项采用牛顿迭代法,导出离散的线性代数方程组.最后,通过数值算例验证配点法格式的精度及能量递减规律.
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| 关 键 词： | Allen-Cahn方程 有限差分法 重心插值配点法 Newton迭代格式 能量递减 |
Two Dimensional Allen-Cahn Equation Solved By FiniteDifference Method/Collocation Method |
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| DENG Yangfang,YAO Zefeng,WANG Jingying,WENG Zhifeng.Two Dimensional Allen-Cahn Equation Solved By FiniteDifference Method/Collocation Method[J].Journal of Huaqiao University(Natural Science),2020,41(5):690-694. |
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| Authors: | DENG Yangfang YAO Zefeng WANG Jingying WENG Zhifeng |
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| Institution: | School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China |
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| Abstract: | Finite difference method is used in time and barycentric interpolation collocation method is used in space for the solution of two dimensional Allen-Cahn equation. The nonlinear term is discretized by Newton iteration method, the concerned equation derives discrete linear algebraic equations. Finally, numerical examples are given to verify the accuracy and the law of energy decline of the collocation scheme. |
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| Keywords: | Allen-Cahn equation finite difference method barycentric interpolation collocation method Newton iterative scheme energy decline |
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