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解扩散方程的指数时间差分方法
EXPONENTIAL TIME DIFFERENCE METHOD TO SOLVE THE DIFFUSION EQUATION
查看参考文献10篇
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文摘
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指数时间差分方法是近年来提出求解刚性常微分方程的一种新的数值计算方法.指数时间差分方法是一种积分方法,而不是经典的差分方法.利用指数时间差分方法求解扩散方程,如一维拟线性对流扩散方程和Allen-Cahn扩散方程.扩散方程在空间方向离散后转化成刚性常微分方程.用显式指数时间差分方法和相应阶的显式Runge-Kutta方法求解刚性常微分方程.数值结果表明显式指数时间差分方法具有相同阶的显式Runge-Kutta方法相应的精度,稳定性显著提高,而且能很好地模拟扩散方程的演化行为.指数时间差分方法可用于刚性常微分方程的数值计算. |
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其他语种文摘
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Exponential time difference method is a kind of new numerical computational method, which was proposed to solve the stiff ordinary differential equations recently.Exponential time difference method is a kind of integrator method,which is not the classical difference method.The diffusion equations,such as the one dimensional quasi-linear advection diffu- sion equation and the Allen-Cahn diffusion equation,were solved by the exponential time difference method.The diffusion equation was discretizated in the spacial direction and transformed into the stiff ordinary differential equations.The explicit exponential difference time method and the corresponding explicit Runge-Kutta method were applied to solve the stiff ordinary differential equations.Numerical results showed that the explicit exponential time difference method has the same accuracy as the corresponding explicit Runge-Kutta method and better stability,moreover can well simulate the evolution behaviors of the diffu- sion equations.The exponential time difference method can be applied to simulate the stiff ordinary differential equations. |
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来源
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数值计算与计算机应用
,2008,29(4):261-266 【核心库】
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关键词
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扩散方程
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指数时间差分方法
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Runge-Kutta方法
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稳定性
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地址
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1.
北京应用物理与计算数学研究所, 北京, 100191
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中国科学院计算数学研究所, 北京, 100190
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北京服装学院基础教学部, 北京, 100029
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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1000-3266 |
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学科
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数学 |
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基金
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国家自然科学基金
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文献收藏号
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CSCD:3427077
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参考文献 共
10
共1页
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1.
Magnus W. On the exponential solution of differential equations for a linear operators.
Comm Pure Appl Math, Ⅶ,1954:649-673
|
被引
17
次
|
|
|
|
|
2.
Iserles A. Lie Group Methods.
Acta Numeric,2000:215-365
|
被引
30
次
|
|
|
|
|
3.
Cox S M. Exponential time differencing for stiff systems.
J. Comp. Phys.,2002,176:430-455
|
被引
20
次
|
|
|
|
|
4.
Sun Jianqiang. RKMK method of solving non-damping LL equations and ferromagnet chain equations.
Applied Mathematcis and computation,2004,157:407-424
|
被引
3
次
|
|
|
|
|
5.
Hairer E.
Solving Ordinary Differential EquationsⅡ:Stiff and Differential Algebraic Problems,1999
|
被引
1
次
|
|
|
|
|
6.
Beyklin G. A new class of time discretization scheme for the solution of nonlinear PDEs.
J. Comp. Phys.,1998,147:362-387
|
被引
1
次
|
|
|
|
|
7.
Gear W. Projective Methods for Stiff Differential Equations:Problems with Gaps in Their Eigenvalue SPectral.
SIAM Journal on Scientific Computing,2003,24:1091-1106
|
被引
2
次
|
|
|
|
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8.
Vanden Berghe G. Frequency determination and step-length control for exponentially-fitted Runge-Kutta methods.
Journal of Computational and Applied Mathematics,2001,132:95-105
|
被引
3
次
|
|
|
|
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9.
Du Qiang. Stability analysis and application of the exponential time differencing scheme.
Journal of Computation Mathematicsm,2004,22(2)
|
被引
1
次
|
|
|
|
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10.
吴永. 流形上微分方程的算法.
数学进展,35(4):385-394
|
被引
1
次
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