基于时间-空间谱配法的分数阶微分方程的一种解法  

A Solution of Fractional Differential Equations on Time-space Spectrum Allocation Method

作　　者：王龙[1] 赵丹[1] WANG Long;ZHAO Dan(Sichuan Vocational&Technical College,Suining 629000,China)

机构地区：[1]四川职业技术学院,四川遂宁629000

出　　处：《山东农业大学学报（自然科学版）》2019年第1期142-144,共3页Journal of Shandong Agricultural University：Natural Science Edition

基　　金：四川省教育厅一般基金项目:偏微分方程图像分割算法研究(15ZB0358)

摘　　要：随着分数阶微分方程的应用领域越来越广泛,相应的理论研究也变得更加重要。本文针对时间分数阶的经典微分方程,提出一种加入空间谱配的解法。通过对时间分数阶经典微分方程的推导,得出等价的微分方程并获取空间配置点,然后应用高斯积分公式转变空间,求出转换方程的积分项。数值验算结果表明:采用时间-空间谱配法得出的精确解与数值解吻合程度较好,基本能满足分数阶微分方程高精度近似解的要求。With the application of fractional differential equation more and more widely,the corresponding theoretical research has become more important.In this paper,we propose a solution to the classical differential equation of fractional order in time by adding spatial spectral assignment.By deducing the classical differential equation of time fractional order,the equivalent differential equation is obtained and the spatial collocation points are obtained.Then the integral terms of the transformation equation are obtained by applying the Gauss integral formula to transform the space.The numerical results show that the exact solution obtained by the time-space spectrum matching method is in good agreement with the numerical solution,and can basically meet the requirements of high-precision approximate solution of fractional differential equation.

关 键 词：分数阶微分方程 时间-空间谱配法 精确解 数值解 

分 类 号：O29[理学—应用数学]