一类分数阶Langevin方程卷积算法的数值分析
首发时间:2018-12-17
摘要:将分数阶算子加入Langevin方程,得到一类具有时间记忆性的Langevin方程。利用卷积算法得到方程数值解,并给出其收敛性和稳定性分析。理论分析和数值试验误差分析均证实,卷积算法的数值解是收敛且稳定的,表明本文用卷积算法求解一类分数阶Langevin方程是高效可行的。
关键词: 分数阶Langevin方程 卷积算法 收敛性 稳定性 数值试验
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Numerical analysis of a class of fractional Langevin equations by convolution algorithm
Abstract:The fractional order operator is added to the Langevin equation to obtain a class of time-memory fractional Langevin equations.The numerical solution of the equation is obtained by convolution algorithm,and the convergence and stability analysis are given.Both theoretical analysis and numerical experiments\' error analysis show that the numerical solution by convolution algorithm is convergent and stable.It is shown that the convolution algorithm is efficient and feasible for solving the class of fractional Langevin equation.
Keywords: Fractional Langevin equation Convolution algorithm Convergence Stability Numerical experiments
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