Context This study primarily investigates the changes in carbon adsorption capacity and hydrogen adsorption capacity on the anode catalyst surface when using methane fuel and mixed gas fuel as the anode fuel for SOFC systems. To reduce the carbon adsorption capacity of the commonly used anode catalyst—nickel-based catalysts—towards hydrocarbon fuels, copper and gold are doped into the nickel-based catalysts to compare the effects on carbon and hydrogen adsorption capacities. Moreover, aside from calculating the carbon and hydrogen adsorption capacities, this project also evaluates the impact of mixed gas effects and doping effects on SOFC performance through the analysis of hydrogen diffusion coefficients and performance polarization curves. The findings reveal a noteworthy enhancement in the diffusion coefficient of syngas within the Au-doped Ni catalyst, showing an improvement of up to 45.46% at 973 K. Furthermore, the electrical power generated by syngas in the Au-doped Ni catalyst at 973 K demonstrates an increase of up to 12.06%. Methods This study primarily employs DFT to calculate the carbon and hydrogen adsorption energies on methane, utilizing CASTEP for the calculations. During these calculations, the adsorption energy is determined through a three-layer surface approach, in conjunction with the Kohn–Sham equations, combining the Generalized Gradient Approximation and ultrasoft pseudopotentials for TS-search calculations. On the other hand, this project will analyze the diffusion coefficient of hydrogen on the anode catalyst using MD methods combined with the ReaxFF potential field, with GULP being utilized to complete all dynamics calculation theories. Finally, the project will analyze the performance of SOFC cells, incorporating relevant numerical equations with Matlab for numerical analysis.