## The approximate solutions of time-fractional diffusion equation by using Crank-Nicolson method.(English)Zbl 1349.65274

Summary: We consider approximate solution of time-fractional diffusion equation (TFDE) by using Crank-Nicolson method. Besides, we utilize property of Riemann-Liouville derivative to obtain this solution. Then, we draw three dimensional graphics of this solution by means of programming language Mapple. Finally, we show table including error $$\alpha$$, $$x$$, $$t$$, $$M$$ and $$N$$. Numerical results ensure to illustrate the effectiveness and reliability of this method.

### MSC:

 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35K05 Heat equation