In this paper, we discuss the opinion dynamics of a social network by using the Shooting method based on Newton's iteration upon differential game framework. The technique applies to nonlinear and time-varying systems with non-convex structures as well. This technique consists of three stages. First of all, the analytic solution is obtained for an initial co-state estimate. Secondly, the error of the terminal condition is computed. Finally, the error of the terminal condition is reduced by going one iteration in Newton's method. The effectiveness of the algorithm has been demonstrated for a differential game problem with a leader-follower information structure. The flexibility and the generality of the algorithm indicate that it is a highly promising method.