Analysis for one-dimensional time-fractional Tricomi-type equations by LDG methods

作者：Zhang Xindong^*; Liu Juan; Wen Juan; Tang Bo; He Yinnian

来源：Numerical Algorithms, 2013, 63(1): 143-164.

DOI：10.1007/s11075-012-9617-3

• Linear time-fractional Tricomi-type equation
• Local discontinuous Galerkin finite element method
• Caputo fractional derivative
• Fractional differential equation

In this paper, we consider the local discontinuous Galerkin (LDG) finite element method for one-dimensional linear time-fractional Tricomitype equation (TFTTE), which is obtained from the standard one-dimensional linear Tricomi-type equation by replacing the first-order time derivative with a fractional derivative (of order alpha, with 1 < alpha <= 2). The proposed LDG is based on LDG finite element method for space and finite difference method for time. We prove that the method is unconditionally stable, and the numerical solution converges to the exact one with order O(h(k+1) + tau(2)), where h, tau and k are the space step size, time step size, polynomial degree, respectively. The comparison of the LDG results with the exact solutions is made, numerical experiments reveal that the LDG is very effective.

• 出版日期2013-5
• 单位新疆大学; 西安交通大学; 新疆师范大学