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.

中文翻译：

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多维分数阶对流扩散方程第一初边值问题的局部一维格式

摘要

研究了分数阶对流扩散方程的第一边值问题。构建了局部一维差分方案。使用最大值原理，在统一度量中获得先验估计。证明了差分格式的稳定性和收敛性。构造了局部一维差分格式的近似解算法。进行了说明工作中获得的理论结果的数值计算。