Incorporating detailed chemistry in solvers still remains a daunting and intractable task due to the prohibitive computational cost. However the combination of advanced mathematical solution techniques such as tabulation and calculating the analytical Jacobian in combination with efficient computational techniques that use the graphical processing unit (GPU) to do calculations can drastically speedup the simulation. These techniques are not mutually exclusive as is demonstrated for an ordinary differential equation (ODE) problem describing the classical adiabatic, constant-volume ignition of an equimolar methane/air mixture. Acceleration with up to a factor 120 can be obtained with the new algorithm compared to the algorithm employed in the reference solver. Maximum speedup is obtained in the case where the analytical Jacobian and the rates are calculated using the GPU when using intrinsic compiler functions to calculate transcendental functions which are used to calculate thermodynamic and kinetic coefficients. This is because the GPU can calculate transcendental functions significantly more efficient than a CPU.