Local one-dimensional scheme for the first initial-boundary value problem for the multidimensional fractional-order convection–diffusion equation

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