A finite difference method for fractional partial differential equation

作者：Zhang Yang^*

来源：Applied Mathematics and Computation, 2009, 215(2): 524-529.

DOI：10.1016/j.amc.2009.05.018

• Partial differential equation
• Space-time fractional derivative
• Finite difference method
• Stability
• Convergence
• Error estimates

An implicit unconditional stable difference scheme is presented for a kind of linear space time fractional convection-diffusion equation. The equation is obtained from the classical integer order convection-diffusion equations with fractional order derivatives for both space and time. First-order consistency, unconditional stability, and first-order convergence of the method are proven using a novel shifted version of the classical Grunwald finite difference approximation for the fractional derivatives. A numerical example with known exact solution is also presented, and the behavior of the error is examined to verify the order of convergence.

• 出版日期2009-9-15
• 单位南开大学