一类分数阶Cattaneo方程Neumann边值问题的紧致差分格式

A COMPACT DIFFERENCE SCHEME FOR A CLASS OF FRACTIONAL CATTANEO EQUATION WITH NEUMANN BOUNDARY CONDITIONS

为了更好地描述非傅里叶热传导现象,从广义的Cattaneo模型出发,得到分数阶Cattaneo方程的数值解,考虑一类分数阶Cattaneo方程Neumann边值问题的数值模拟.采用Caputo分数阶导数L1插值逼近和空间离散的方法,对所研究的边值问题的方程建立时间具有3-α阶精度,空间具有4阶精度的紧致差分格式;数值算例验证了理论分析结果,证明了对分数阶Cattaneo方程Neumann边值问题所建立的离散格式的稳定性和有效性.

In order to better describe the non-Fourier heat conduction phenomenon,the numerical solution of fractional Cattaneo equation is obtained from the generalized Cattaneo model,and the numerical simulation of Neumann boundary value problem for a class of fractional Cattaneo equation is considered.The method of Caputo fractional derivative L1 interpolation approximation and spatial dispersion is used to establish the equation with 3-αorder accuracy in time and 4-order accuracy in space;Numerical results are conducted to verify the theoretical results of the presented scheme.