Abstract: The nonlinear complex parabolic partial differential equation is solived by the predictor-correction scheme. The numerical solutions are attained for the nonlinear propagration of ALFVEN wave-packet in collisional plasmas. The results show the effect of collision damping can not be neglected, whereas the nonlinear Landau damping is a weak effect compared with the collision one.

Key words: predictor-correction scheme, nonlinear complex parabolic equation, ALFVEN wave, collision-damping, nonlinear Landau damping