The present paper deals with some mathematical aspects of generalized time-dependent Ginzburg-Landau theories for the numerical simulation of mesoscale phase separation kinetics of copolymer melts. We shortly discuss the underlying theory and introduce an expansion of the external potential, to be used in the dynamics algorithm, which is similar to free-energy expansions. This expansion is valid for both compressible and incompressible multicomponent copolymer melts using a Gaussian chain model. The expansion is similar to the well-known random phase approximation (RPA) but differs in some important aspects. Also, the application of RPA like free energy expansions to dynamics is new. Our derivation leads to simple expressions for the vertex coefficients, which enables us to numerically calculate their full wave Vector dependence, without assuming an ordered morphology. We find that our fourth-order vertex is negative for some wave vectors which has important consequences for the simulation of mesoscopic dynamics. We propose a fitting procedure for the vertex coefficients to overcome the computationally expensive calculation of the linear and bilinear expansion terms in the expansion, This procedure provides analytically derived parameters for a gradient free energy expansion, which allows for a whole new class of phase-separation models to be defined.