Tanh method (or hyperbolic tangent) method is considered as analytic methods because a whole range of analytical solution methods such as Hirota’s bilinear technique, inverse scattering transform , PainlevBe analysis , etc.were developed. Please look at the following below attached file which may help you in your issue.
A given method is analytical one if it diagnoses, senses and quantifies a physical parameter in numerical terms which may be very handy in making a decision in qualitative terms. So a method confirming to the abovesaid requirements should come in the ambit of analytical one. The method you referred has both connotations.