Mathematical models of self-igniting reaction diffusion systems are discussed theoretically. The model comprises a system of reaction-diffusion equations that are nonlinearly connected. The efficient and easily accessible analytical technique AGM was used to solve the steady-state non-linear equations for a self-igniting reaction diffusion system. The proposed method’s efficiency and accuracy will be tested against some of the widely used numerical approaches found in the literature Herein, we present the generalized approximate analytical solution for the concentration of gas reactant and temperature for the experimental values of heat of reaction, thermal Thiele modulus and activation energy parameters. Using the Matlab / Scilab program, we also derive the numerical solution to this problem. Simulated data and previously published limiting cases are used to validate the new analytical results. A reasonable agreement is observed.