Research paperA compact finite difference scheme for variable order subdiffusion equation

•A new second order numerical approximation to the variable order time Riemann-Liouville derivative is derived, and a Crank-Nicolson type compact finite difference scheme with second order temporal accuracy and fourth order spatial accuracy for time variable order subdiffusion equation is presented.•The unconditional stability and convergence of the proposed scheme is strictly proved by using the discrete energy method.•Numerical results confirm our theoretical analysis, and demonstrate the effectiveness of the compact finite difference scheme.

In this paper, we consider a variable order time subdiffusion equation. A Crank-Nicolson type compact finite difference scheme with second order temporal accuracy and fourth order spatial accuracy is presented. The stability and convergence of the scheme are strictly proved by using the discrete energy method. Finally, some numerical examples are provided, the results confirm the theoretical analysis and demonstrate the effectiveness of the compact difference method.