A novel equivalent definition of Caputo fractional derivative without singular kernel and superconvergent analysis

作者：Liu, Zhengguang; Li, Xiaoli^*

来源：Journal of Mathematical Physics, 2018, 59(5): 051503.

DOI：10.1063/1.4993817

• FINITE DIFFERENCE/SPECTRAL APPROXIMATIONS
• REACTION-DIFFUSION EQUATION
• ELEMENT-METHOD
• VOLUME METHOD
• TIME
• TRANSPORT
• MODELS

In this article, we present a new second-order finite difference discrete scheme for a fractal mobile/immobile transport model based on equivalent transformative Caputo formulation. The new transformative formulation takes the singular kernel away to make the integral calculation more efficient. Furthermore, this definition is also effective where alpha is a positive integer. Besides, the T-Caputo derivative also helps us to increase the convergence rate of the discretization of the alpha-order( 0 < alpha < 1) Caputo derivative from O(tau(2-alpha)) to O(tau(3-alpha)), where tau is the time step. For numerical analysis, a Crank-Nicolson finite difference scheme to solve the fractal mobile/immobile transport model is introduced and analyzed. The unconditional stability and a priori estimates of the scheme are given rigorously. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis. Published by AIP Publishing.

• 出版日期2018-5
• 单位山东大学