| 利用Laplace变换求解分数阶Allen-Cahn方程 |
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| 引用本文： | 汪精英,邓杨芳,翟术英.利用Laplace变换求解分数阶Allen-Cahn方程[J].华侨大学学报(自然科学版),2020,41(4):549-554. |
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| 作者姓名： | 汪精英 邓杨芳 翟术英 |
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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： | 创新人才计划;华侨大学研究生科研创新能力培养计划项目;国家自然科学基金 |
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| 摘 要： | 考虑Caputo型分数阶Allen-Cahn方程的高效数值算法,利用Laplace变换将其转化为整数阶Allen-Cahn方程.利用算子分裂方法进一步将其分解为热传导方程和非线性方程.其中,非线性方程精确求解,热传导方程采用二阶差分方法求解.数值实验表明了所给格式的有效性.
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| 关 键 词： | 分数阶Allen-Cahn方程 Caputo型分数阶导数 Laplace变换 算子分裂 能量递减 |
Numerical Solution of Fractional Allen-Cahn Equation byLaplace Transform |
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| WANG Jingying,DENG Yangfang,ZHAI Shuying.Numerical Solution of Fractional Allen-Cahn Equation byLaplace Transform[J].Journal of Huaqiao University(Natural Science),2020,41(4):549-554. |
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| Authors: | WANG Jingying DENG Yangfang ZHAI Shuying |
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| Institution: | School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China |
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| Abstract: | An efficient numerical algorithm for Caputo-type fractional Allen-Cahne quation is considered. Firstly, the Laplace transform is used to transform it into integer order Allen-Cahn equation, and then the operator splitting method is used to decompose into heat conduction equation and nonlinear equation. The nonlinear equation is solved analytically and the heat conduction equation is solved using second-order finite difference method. Numerical experiments are presented to confirm the efficiency of the proposed method. |
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| Keywords: | fractional Allen-Cahn equation Caputo-type fractional derivative Laplace transform operator splitting method energy decline |
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