ERROR ANALYSIS OF DISCONTINUOUS GALERKIN METHOD FOR THE TIME FRACTIONAL KDV EQUATION WITH WEAK SINGULARITY SOLUTION

In this work, the time fractional KdV equation with Caputo time derivative of order alpha is an element of (0, 1) is considered. The solution of this problem has a weak singularity near the initial time t = 0. A fully discrete discontinuous Galerkin (DG) method combining the well-known L1 discretisation in time and DG method in space is proposed to approximate the time fractional KdV equation. The unconditional stability result and O(N--min{r alpha,N-2-alpha}+ h(k+1)) convergence result for P-k (k >= 2) polynomials are obtained. Finally, numerical experiments are presented to illustrate the efficiency and the high order accuracy of the proposed scheme.