Digital simulation of guitar tube amplifiers is still an opened topic. The efficient implementation of several parts of the guitar amplifier is presented in this paper. This implementation is based on the pre-computation of the solution of the nonlinear differential system and further approximation of the solution. It reduces the computational complexity while the accuracy is comparable with the numerical solution. The method is used for simulation of different parts of the guitar amplifier, namely a triode preamp stage, a phase splitter and a push-pull amplifier. Finally, the results and comparison with other methods are discussed.