The Time Domain Boundary Element Method (TDBEM) has its advantages in the analysis of transient electromagnetic fields (wake fields) induced by a charged particle beam with curved trajectory in a particle accelerator. On the other hand, the TDBEM has disadvantages of huge required memory and computation time compared with those of the Finite Difference Time Domain (FDTD) method or the Finite Integration Technique (FIT). This paper presents a comparison of the FDTD method and 4-D domain decomposition method of the TDBEM based on an initial value problem formulation for the curved trajectory electron beam, and application to a full model simulation of the bunch compressor section of the high-energy particle accelerators.