NON-ITERATIVE DOMAIN DECOMPOSITION METHOD FOR THE CONVECTION–DIFFUSION EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

Abstract

This paper proposes a numerical method based on domain decomposition to find approximate solutions for one-dimensional convection–diffusion equations with Neumann boundary conditions. First, the equations are transformed into convection–diffusion equations with Dirichlet conditions. Second, the author introduces the Prediction/Correction Domain Decomposition (PCDD) method and estimates errors for the interface prediction scheme, interior scheme, and correction scheme using known error estimations. Finally, the author compares the PCDD algorithm with the fully explicit scheme (FES) and the fully implicit scheme (FIS) using three examples. In comparison to FES and FIS, the proposed PCDD algorithm demonstrates good results.