This paper introduces a monotonic weighted compact finite difference scheme (WC-FDM) designed to solve the non-linear 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 in the computational stability regardless of the advection-dominance level and grid spacing uniformity.
Chivapornthip, P. (2025). A monotonic weighted compact finite difference solution for a non-linear steady advection-diffusion equation. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2024.61722.2680
MLA
Chivapornthip, P. . "A monotonic weighted compact finite difference solution for a non-linear steady advection-diffusion equation", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2024.61722.2680
HARVARD
Chivapornthip, P. (2025). 'A monotonic weighted compact finite difference solution for a non-linear steady advection-diffusion equation', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2024.61722.2680
CHICAGO
P. Chivapornthip, "A monotonic weighted compact finite difference solution for a non-linear steady advection-diffusion equation," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2024.61722.2680
VANCOUVER
Chivapornthip, P. A monotonic weighted compact finite difference solution for a non-linear steady advection-diffusion equation. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2024.61722.2680
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