随机Ginzburg-Landau方程的数值模拟
首发时间:2009-04-14
摘要:本文利用有限差分方法数值模拟带可加白噪声类型扰动的Ginzburg-Landau方程。对时间和空间的离散采用对称Crank-Nicolson格式,构造确定性Ginzburg-Landau方程的差分格式,再给出加性噪声精确的数学定义,对加性噪声进行正则化,把加性噪声转化成一列服从标准正态分布的独立随机变量,随机Ginzburg-Landau方程就转化成代数方程组,采用迭代方法解这个代数系统,最后利用Matlab实现可视化,模拟出不同振幅的噪声对孤波的影响,数值结果表明加性噪声不影响孤波的传播,但能增大孤波的振幅,我们认为这是由于噪声起注入能量的作用,使得孤波的振幅增大。
关键词: 随机Ginzburg-Landau方程 差分格式 加性噪声
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Numerical simulation of stochastic Ginzburg-Landau equation
Abstract:In this paper, we numerically investigate Ginzburg-Landau equation with stochastic contribution which is of additive white noise type. Our numerical method is based on difference method.We use finite difference in both time and space with a symmetric Crank-Nicolson discretisation to construct the difference scheme of deterministic Ginzburg-Landau equation.Then we give a precise mathematical definition of additive noise and the noise can be changed into a sequence of independent random variables with normal law.So the stochastic Ginzburg-Landau equation are changed into algebraic equations.We use iteration method to solve the algebraic system.Lastly,We present numerical experiments for different values of noise amplitude and show that an additive noise does not influence the propagation of the wave, but has an increasing effect on the amplitude of the wave.We think that is probably linked to the injection of mass in this case.
Keywords: stochastic Ginzburg-Landau equation difference scheme additive noise
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