A second order Crank-Nicolson scheme for fractional Cattaneo equation based on new fractional derivative

作者：Liu, Zhengguang; Cheng, Aijie^*; Li, Xiaoli

来源：Applied Mathematics and Computation, 2017, 311: 361-374.

DOI：10.1016/j.amc.2017.05.032

• Second order
• New fractional derivative
• Crank-Nicolson
• Cattaneo equation
• Finite difference

Recently Caputo and Fabrizio introduce a new derivative with fractional order which has the ability to describe the material heterogeneities and the fluctuations of different scales. In this article, a Crank-Nicolson finite difference scheme to solve fractional Cattaneo equation based on the new fractional derivative is introduced and analyzed. Some a priori estimates of discrete L-infinity(L-2) errors with optimal order of convergence rate O(tau(2) + h(2))) are established on uniform partition. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

• 出版日期2017-10-15
• 单位山东大学