Particle accelerators are among the most complicated contemporary devices and consist of a large number of components, each with a specific function. All components need to be tuned with respect to each other to achieve the prescribed particle beam characteristics. Seemingly small deviations from the components design specifications may induce irreversible aberration from the particle beam characteristics in subsequent accelerator components. Therefore both fast and accurate beam dynamics simulations of the accelerator as a whole are indispensable during design and operation of a particle accelerator. This thesis is devoted to the further development of beam dynamics simulations on the basis of the moment method, the Vlasov equation, surrogate field models obtained from electromagnetic field simulations and to the application thereof to Radio Frequency Quadrupoles (RFQs). In particular the thesis develops and validates standardised procedures for extracting accurate and reproducible surrogate field models from 3D electromagnetic field simulation results of several accelerator components (radio frequency cavities, solenoids, steerer magnets, Wien filters, dipole magnets, quadrupole magnets, sextupole magnets and octupole magnets). Furthermore an existing Vlasov solver for electrons is extended for the more general case of particles with an arbitrary charge and mass. Highly accurate CAD modelling tools have been developed, defining the modulated rods and the stems of an RFQ on the basis of the design specifications. Surrogate field models dedicated to the RFQs radial matcher cells, transition cells and cells for particle bunching, focussing and acceleration are built. They are derived from 3D electrostatic field simulation results of parts of the RFQ and their accuracy and robustness is validated thoroughly, both with theoretical and realistic RFQ models. The four-rod RFQ design for the 600 MeV proton accelerator as a segment of the MYRRHA research reactor, planned at SCKCEN, was employed as a realistic RFQ validation model. The surrogate field models are implemented into the Vlasov solver. The extended Vlasov solver in combination with the accurate surrogate field models calculates the beam dynamics in an RFQ in a few seconds, making the solver a valuable tool for the design and operation of RFQs.