Fast methods for solving nonlinearly coupled equations describing fiber amplifiers

A series of fast and accurate methods for ordinary differential equations are proposed. The results of solving nonlinearly coupled equations describing fiber Raman amplifiers demonstrate that these methods can improve the accuracy by more than one or even two orders of magnitude in comparison with the classical methods, and can increase the computing speed by more than an order of magnitude on the same accuracy. The proposed methods can availably solve nonlinearly coupled equations of erbium-doped fiber amplifiers.