A novel numerical scheme for reproducing kernel space of 2D fractional diffusion equations

A novel method is presented for reproducing kernel of a 2D fractional diffusion equation. The exact solution is expressed as a series, which is then truncated to get an approximate solution. In addition, some techniques to improve existing methods are also proposed. The proposed approach is easy to implement. It is proved that both the approximate solution and its partial derivatives converge to their exact solutions. Numerical results demonstrate that the proposed approach is effective and can provide a high precision global approximate solution.