On high order numerical schemes for fractional differential equations by block-by-block approach

The exact solutions to nonlinear fractional problems usually have initial singularity. Taking the singularity into account, the change of variable and the block-by-block approach are introduced to propose a novel high-order scheme. It is proved that our proposed scheme can be of order 3+α under the non-smooth solutions. Numerical examples are shown to validate our theoretical results.