| 时间分数阶Allen-Cahn方程的重心插值配点法 |
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| 引用本文： | 黄蓉,翁智峰.时间分数阶Allen-Cahn方程的重心插值配点法[J].华侨大学学报(自然科学版),2022,0(4):553-560. |
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| 作者姓名： | 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基金资助项目（ZQN-702）； |
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| 摘 要： | 采用Laplace变换近似Caputo型分数阶导数,将分数阶方程转换成整数阶方程;然后,在时-空方向均采用重心插值配点法离散,非线性项采用Newton迭代格式求解,并给出配点格式的相容性误差分析.数值实验表明:该配点法格式具有较高精度,能满足能量递减规律.
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| 关 键 词： | Caputo型分数阶 Allen-Cahn方程 Laplace变换 重心插值配点法 误差分析 能量递减 |
Barycentric Interpolation Collocation Method for Time-Fractional Allen-Cahn Equation |
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| HUANG Rong,WENG Zhifeng.Barycentric Interpolation Collocation Method for Time-Fractional Allen-Cahn Equation[J].Journal of Huaqiao University(Natural Science),2022,0(4):553-560. |
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| Authors: | HUANG Rong WENG Zhifeng |
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| Institution: | School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China |
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| Abstract: | The Laplace transform is uesd to approximate the Caputo-type fractional derivative and transform the time-fractional Allen-Cahn equation into the integer order case. Then, the barycentric interpolation collocation method is used to discretize integer order Allen-Cahn equation in both time and space directions, the nonlinear term is solved by Newton iteration method. Moreover, error estimates of the collocation scheme are also presented. Numerical experiments are presented to verify the high accuracy and satisfying the law of energy decline for the collocation scheme. |
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| Keywords: | Caputo-type fractional Allen-Cahn equation Laplace transform barycentric interpolation collocation method error analysis energy decline |
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