Contents I. Introduction
The nonstationary electrodynamics describes the excitation and propagation of nonstationary waves or pulses in different structures: multilayered, periodic (photonic crystals, slowwave structure), waveguides, resonators, waveguide transformers (multiports), and in media, including dispersive, dissipative, active, and nonlinear ones. So, the main goal is to obtain and solve the wave excitation and propagation equations. There are different approaches to solve this problem, for example, the direct solution of Maxwell equations using FDTD [1]. But, in our opinion, the more constructive method for certain problems with not very complicated boundaries is the solution of spatial-time integral or integrodifferential equations (STIEs, STIDEs). Inasmuch as such equations are based on Green's function (GF) approach, the causal and radiation conditions are automatically satisfied, and the method is very appropriate to open structures. In this case free-space GFs [3] may be used, so the method also is universal. There are some limitations for structures with incoordinate boundaries when the GFs are unknown and the STIEs based on free-space GFs are complicated. The considered methods demand minimal computational resources and may be realized using the application of finite elements or finite integration to STIEs.
