In this paper, the Heisenberg ferromagnetic spin chain equation, which is a model with different magnetic interactions in the classical and semiclassical limits, is investigated using the generalized exponential rational function method. The reduction of the governing equation to a simpler ordinary differential equation by wave transformation is the first step of the procedure. A plurality of the exact solution is obtained by using the relevant method. Physical interpretations of some obtained solutions are also included. Particularly, upon choosing appropriate parameters, various plots are depicted. We achieve also a numerical solution corresponding to the initial value problem by the Elzaki–Adomian decomposition method and give comparative results in a table. Moreover, by using Maple, some graphical simulations are done to see the behavior of these solutions with choosing the suitable parameters.