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Due to the high importance of the convection-diffusion equation, we aim to develop a quadratic upwind differencing scheme in the finite volume approach for solving this equation. Our newly developed numerical approach is conditionally stable. The strategy employs a quadratic upwind differencing scheme in the finite volume technique for spatial approximation with third-order accuracy. The temporal integration is approximated using the explicit theta method of first-order accuracy. Some numerical examples are given to support our theoretical procedures. The findings are plotted using MATLAB R2016a mathematical software.

Quadratic upwind differencing scheme in the finite volume method for solving the convection-diffusion equation