利用Laplace变换求解时间分数阶Swift-Hohenberg方程
Solving Time Fractional Swift-Hohenberg Equation Using Laplace Transform
DOI: 10.12677/AAM.2021.105179, PDF,    科研立项经费支持
作者: 项诗景, 王倩倩：华侨大学数学科学学院，福建 泉州；谢 歆：黄山学院数学与统计学院，安徽 黄山
关键词: Swift-Hohenberg方程；Laplace变换；算子分裂法；Crank-Nicolson差分格式；Swift-Hohenberg Equation； Laplace Transform； Operator Splitting Method； Crank-Nicolson Difference Scheme
摘要: 针对时间分数阶Swift-Hohenberg方程，本文提出了基于Laplace变换的高效数值算法。首先利用Laplace变换将原Caputo型分数阶方程转化为整数阶方程，然后利用算子分裂法进一步将其分解成线性方程和非线性方程，其中，非线性方程通过积分法近似求解，线性方程通过Crank-Nicolson差分格式求解，最后通过数值实验验证了所给格式的有效性。
Abstract: For the time fractional Swift-Hohenberg equation, this paper proposes an efficient numerical algorithm based on Laplace transform. First, the Laplace transform is used to transfrom the original Caputo fractional equation into an integer-order equation, and then the operator splitting method is used to further decompose the equation into linear equation and nonlinear equation. The nonlinear equation is approximately solved by the integral method, and the linear equation is solved by the Crank-Nicolson scheme and central difference. Finally, the validity of the given scheme is verified through numerical experiments.
文章引用：项诗景, 王倩倩, 谢歆. 利用Laplace变换求解时间分数阶Swift-Hohenberg方程[J]. 应用数学进展, 2021, 10(5): 1681-1688. https://doi.org/10.12677/AAM.2021.105179

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