A novel finite difference discrete scheme for the time fractional diffusion-wave equation

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

来源：Applied Numerical Mathematics, 2018, 134: 17-30.

DOI：10.1016/j.apnum.2018.07.001

• Fractional derivative
• Diffusion-wave equation
• Novel finite difference
• Numerical experiments
• Estimates

In this article, we consider initial and boundary value problems for the diffusion wave equation involving a Caputo fractional derivative (of order a, with 1 < alpha < 2) in time. A novel finite difference discrete scheme is developed for using discrete fractional derivative at time t(n) in which some new coefficients (k + 1/2)(2-alpha) (k - 1/2)(2-alpha) instead of (k + 1)(2-alpha) - k(2-alpha) are derived. Stability and convergence of the method are rigorously established. We prove that the novel discretization is unconditionally stable, and the optimal convergence orders O (tau(3-alpha) + h(2)) both in L-2 and L-infinity, are derived, where tau is the time step and h is space mesh size. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

• 出版日期2018-12
• 单位山东大学