University of Tabriz Computational Methods for Differential Equations 2345-3982 14 2 2026 04 01 A monotonic weighted compact finite difference solution for a non-linear steady advection-diffusion equation 549 566 19079 10.22034/cmde.2024.61722.2680 EN Prapol Chivapornthip Department of Industrial Engineering, Faculty of Engineering, Kasetsart University, Thailand. Journal Article 2024 05 20 This paper introduces a monotonic weighted compact finite difference scheme (WC-FDM) designed to solve the nonlinear one-dimensional steady advection-diffusion equation (ADE). The WC-FDM scheme is validated against the analytical solution and is adaptable to accommodate both uniform and non-uniform grid spacing. Criteria for selecting weights have been developed to ensure scheme monotonicity. Computational performance is benchmarked against other numerical schemes. Numerical analyses reveal that the WC-FDM accurately solves the non-linear steady ADE for both uniform and non-uniform grid spacing scenarios without introducing spurious oscillations. The proposed weight criteria maintain the monotonicity of the WC-FDM scheme resulting the computational stability regardless of the advection dominance level and grid spacing uniformity. https://cmde.tabrizu.ac.ir/article_19079_96ef5a63bf8ac128cdc882208a65e0d5.pdf