  Frequently we revise our first opinions after talking over with other
individuals because we get convinced. Argumentation is a verbal and social
process aimed at convincing. It includes conversation and persuasion. In this
case, the agreement is reached because the new arguments are incorporated. In
this paper we deal with a simple model of opinion formation with such
persuasion dynamics, and we find the exact analytical solutions for both, long
and short range interactions. A novel theoretical approach has been used in
order to solve the master equations of the model with non-local kernels.
Simulation results demonstrate an excellent agreement with results obtained by
the theoretical estimation.
