Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations

作者：Liu, Yanmei; Khan, Monzorul; Yan, Yubin^*

来源：Mathematics, 2016, 4(3): 45.

DOI：10.3390/math4030045

• space-fractional partial differential equations
• stochastic partial differential equations
• Fourier spectral method
• error estimates

Fourier spectral methods for solving some linear stochastic space-fractional partial differential equations perturbed by space-time white noises in the one-dimensional case are introduced and analysed. The space-fractional derivative is defined by using the eigenvalues and eigenfunctions of the Laplacian subject to some boundary conditions. We approximate the space-time white noise by using piecewise constant functions and obtain the approximated stochastic space-fractional partial differential equations. The approximated stochastic space-fractional partial differential equations are then solved by using Fourier spectral methods. Error estimates in the L-2-norm are obtained, and numerical examples are given.

• 出版日期2016-9
• 单位吕梁学院