Unique solvability of the CCD scheme for convection–diffusion equations with variable convection coefficients

Abstract

Abstract The combined compact difference (CCD) scheme has better spectral resolution than many other existing compact or noncompact high-order schemes, and is widely used to solve many differential equations. However, due to its implicit nature, very little theoretical results on the CCD method are known. In this paper, we provide a rigorous theoretical proof for the unique solvability of the CCD scheme for solving the convection-diffusion equation with variable convection coefficients subject to periodic boundary conditions.

Keywords

• Combined compact difference scheme
• Convection-diffusion equation
• Unique solvability
• Variable coefficient
• Periodic boundary conditions