加热下分数阶广义二阶流体的Stokes第一问题的高阶数值方法  

High-Order Numerical Methods of the Fractional Order Stokes' First Problem for a Heated Generalized Second Grade Fluid

作　　者：叶超[1] 骆先南[1] 文立平[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《应用数学和力学》2012年第1期61-75,共15页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10971175);湖南省教育厅重点科研资助项目(09A093)

摘　　要：针对一类带Dirichlet边值条件和初值条件的加热下分数阶广义二阶流体的Stokes第一问题,提出了一种新的高阶隐式数值格式.应用Fourier分析方法和矩阵方法研究了该格式的稳定性、可解性及收敛性.也进一步给出一个时间误差阶更高的改进的隐式格式.最后通过两个数值算例验证了格式的理论分析是有效可靠的.High-order implicit finite difference methods for solving the Stokes＇ first problem for a heated generalized second grade fluid with fractional derivative were studied. The stability, solvability and convergence of the numerical scheme were discussed via fourier analysis and matrix analysis method. An improved implicit scheme was also obtained. Finally, two numerical examples were presented to demonstrate the effectiveness of the mentioned schemes.

关 键 词：分数阶Stokes问题 隐式差分格式 可解性 稳定性 收敛性 

分 类 号：O241.82[理学—计算数学]