Catalytic combustion is proposed and developed as an efficient method of promoting stability and oxidation of gaseous fuel with minimum pollutants. The effect of catalytic combustion of gaseous turbulent diffusion flames over catalytic discs containing Pt, Pd, and (Pt + Pd) supported on gamma-Al2O3 were experimentally and mathematically studied. These flames have proved to be highly stable over the three catalytic burners and their catalytic enhancement is found to be in the order (Pt + Pd) > Pt > Pd. The axi-symmetric thermal distribution of flames developing over these burners record higher values due to enhancing the fuel oxidizability on the noble metal sites in the reaction zone of flames via improving homogeneous-heterogeneous chemical reactions. Lower values of CO and NO are measured at the axial flames direction in the presence of catalytic burners. A numerical approach has been investigated for the catalytic combustion process on the three noble metals disc burners showing high numerical evaluation of different predicted functions. Stability limits are analyzed following a 1st-degree polynomial. The model of temperatures distribution is described by Gaussian function. For CO distribution, a non-linear four parameters model has been predicted. A differential equation for NO indicates perfectly the location of the peak values. These models have been strictly confirmed with the experimental data.