The convergence of approximate solutions of the Cauchy problem for the model of quasi-steady process in conducting nondispersive medium with relaxation

This article deals with numerical method for solving of the Dirichlet-Cauchy problem for equation modeling the quasi-steady process in conducting nondispersive medium with relaxation. This problem describes a complex electrodynamic process, allows to consider and predict its flow in time. The study of electrodynamic models is necessary for the development of electrical engineering and new energy saving technologies. The main equation of the model is considered as a quasi-linear Sobolev type equation. The convergence of approximate solutions obtained from the use of the method of straight lines with $\varepsilon$-embedding method and complex Rosenbrock method is proven in the article. The lemmas on the local error and on the distribution of error are proven. Estimates of a global error of the method are obtained.