Abstract:
The first boundary value problem for the fractional-order convection–diffusion equation is studied. A locally one-dimensional difference scheme is constructed. Using the maximum principle, a prior estimate is obtained in the uniform metric. The stability and convergence of the difference scheme are proved. An algorithm for the approximate solution of a locally one-dimensional difference scheme is constructed. Numerical calculations illustrating the theoretical results obtained in the work are performed.
Key words:partial differential equation, convection–diffusion equation, fractional-order derivative, fractional time derivative in the Caputo sense, locally one-dimensional difference scheme, stability and convergence of difference schemes.
