Comparison of the FDTD and direct-integrating algorithms for solution of the one-dimensional nonstationary electrodynamic problem

Electromagnetic propagation in media with time-varying parameters is of interest for many applications: shock waves, strong laser fields, nuclear burst, atmospheric or environmental change and others. As a rule, an exact consideration of electromagnetic processes in media with the time-varying parameters is possible in special cases only. In the general case, an initial electromagnetic problem can be investigated by numerical methods. FDTD methods are popular due to their clarity and elegant realization in numerical algorithms. The integral equations approach seems to have a more promising future in terms of both reflection-free realization and stability. An advantage of the integral equation method is that it can be generalized to nonlinear dispersive materials. In this paper both FDTD and the integral equation approaches are investigated, accuracy and stability comparison of these methods are examined. Special computer modeling software is developed for dispatching the numerical experiments