| 重心插值配点法求解Cahn-Hilliard方程 |
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| 引用本文： | 邓杨芳,黄蓉,翁智峰. 重心插值配点法求解Cahn-Hilliard方程[J]. 华侨大学学报(自然科学版), 2022, 43(1): 135-144. DOI: 10.11830/ISSN.1000-5013.202011026 |
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| 作者姓名： | 邓杨芳 黄蓉 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： | 国家自然科学基金资助项目（11701197）;;中央高校基本科研业务费专项资金资助项目（ZQN-702）; |
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| 摘 要： | 对Cahn-Hilliard方程中的时、空方向均采用重心插值配点格式(重心Lagrange插值配点格式和重心有理插值配点格式)进行离散,非线性项采用一般迭代法,导出离散的线性代数方程组,并给出重心Lagrange插值的逼近误差估计.数值算例表明:两种重心插值配点格式均具有高精度,且满足能量递减规律.
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| 关 键 词： | Cahn-Hilliard方程 重心插值配点格式 迭代格式 能量递减 |
Barycentric Interpolation Collocation Method for Cahn-Hilliard Equation |
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| DENG Yangfang,HUANG Rong,WENG Zhifeng. Barycentric Interpolation Collocation Method for Cahn-Hilliard Equation[J]. Journal of Huaqiao University(Natural Science), 2022, 43(1): 135-144. DOI: 10.11830/ISSN.1000-5013.202011026 |
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| Authors: | DENG Yangfang HUANG Rong WENG Zhifeng |
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| Affiliation: | School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China |
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| Abstract: | Barycentric interpolation collocation schemes(barycentric Lagrange interpolation collocation scheme and barycentric rational interpolation collocation scheme)are used to discretize both in time and in space for Cahn-Hilliard equation. The general iteration method is used for the nonlinear term, which derives the discrete linear algebraic equations. Moreover, the error estimation of barycentric Lagrange interpolation method is given. Numerical examples show the high accuracy and the law of energy decline satisfied to the two collocation schemes. |
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| Keywords: | Cahn-Hilliard equation barycentric interpolation collocation scheme iterative scheme energy decline |
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