Analytical solution of -equations in plane geometry

Two analytical methods are used to integrate the system of SN-V1 differential equations with N = 4: 1. 1) Exponential functions 2. 2) Lie series Results of these methods are compared with each other and with those obtained from DTP-IV and other numerical calculations. Comparison shows that 1. 1) Lie series lead to shorter computing times than exponential functions. 2. 2) Lie series are faster than DTF-IV by a factor 7 for a relative accuracy of e = 10−3. This factor increases rapidly for decreasing e. Based on these results it appears profitable to write analytical SN codes (or DSN codes) based on the use of Lie series.