时间分数阶Fokker-Planck方程的Jacobi谱配置方法

Jacobi Collocation Method for Time Fractional Fokker-Planck Equations

分数阶微分方程在工程、生物、金融等领域有广泛的应用.本文利用分数阶积分和微分公式的关系,针对一类带Dirichlet边值条件的时间分数阶Fokker-Planck方程,将其转化为与之等价的带有奇异核的积分微分方程,然后用高斯积分公式数值求解积分项,在时间和空间上都采用Jacobi谱配置法来离散求解积分微分方程.数值算例的结果表明,该方法是非常有效的,数值解具有谱精度,并且该方法容易推广到高维和非线性的情形.

Fractional partial differential equations have recently been applied in various areas of engineering,science,finance,applied mathematics,bioengineering and others.In this paper,we convert the time fractional Fokker-Planck equation into equivalent integral equations with singular kernel,then the model solution is discretized in time and space with a spectral expansion of the Lagrange interpolation polynomial.Numerical results demonstrate the spectral accuracy and efficiency of the collocation spectral method.The proposed technique is not only easy to implement,but also can be easily extended to multidimensional problems.