The dissipative particle dynamics (DPD) simulation method has been used to study mesophase formation of linear (A(m)B(n)) diblock copolymer melts. The polymers are represented by relatively short strings of soft spheres, connected by harmonic springs. These melts spontaneously form a mesocopically ordered structure, depending on the length ratio of the two blocks and on the Flory-Huggins X-parameter. The main emphasis here is on validation of the method and model by comparing the predicted equilibrium phases to existing mean-field theory and to experimental results. The real strength of the DPD method, however, lies in its capability to predict the dynamical pathway along which a block copolymer melt finds its equilibrium structure after a temperature quench. The present work has led to the following results: (1) As the polymer becomes more asymmetric, we qualitatively find the order of the equilibrium structures as lamellar, perforated lamellar, hexagonal rods, micelles. Qualitatively this is in agreement with experiments and existing mean-field theory. After taking fluctuation corrections to the mean field theory into account, a quantitative match for the locations of the phase transitions is found. (2) Where mean-field theory predicts the gyroid phase to be stable, the simulations evolve toward the hexagonally perforated lamellar phase. (3) When a melt is quenched the stable structure emerges via a nontrivial pathway, where a series of metastable phases can be formed before equilibrium is reached. The pathway to equilibrium involves a percolation of the minority phase into a network of tubes, which is destabilized by a nematic or smectic transition. (4) We conclude that either hydrodynamic interactions, or the precise form of the Onsager kinetic coefficient play an important role in the evolution of the mesophases.