Summary: By introducing a simple difference equation to deduce the difference terms and a simple differential equation to deduce the differential terms, we proposed an unified algebraic method for constructing exact solutions to difference-differential equations (DDEs). This method could give many kinds of exact solutions including soliton solutions expressed by hyperbolic functions, periodic solutions expressed by trigonometric functions and rational solutions in a uniform way if solutions of these kinds exist. In this paper, we also give a generalization of the method to determine the degree of DDEs, and compared with the creativity work of D. Baldwin, Ü. Göktas
and W. Hereman
[Comput. Phys. Comm. 162, 203–217 (2004; Zbl 1196.68324
)] through the discrete hybrid equation.