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G. I. Marchuk, “Some Applications of Splitting-up Methods to the Solution of Mathematical Physics Problems,” Aplikace Matematiky, Vol. 1, 1968, pp. 103-132.

has been cited by the following article:

• TITLE: Operator Splitting Method for Coupled Problems:Transport and Maxwell Equations

  AUTHORS: Jürgen Geiser

  KEYWORDS: Operator Splitting Method, Initial Value Problems, Iterative Solver Method, Stability Analysis, Beam Propagation Methods, Transport and Maxwell Equations

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.1 No.3, September 19, 2011

  ABSTRACT: In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor deposition) processes, means the flow of species to a gas-phase, which are influenced by an electric field. Such a field we can model by wave equations. The main contributions are to improve the standard discretization schemes of each part of the coupling equation. So we discuss an improvement with implicit Runge- Kutta methods instead of the Yee’s algorithm. Further we balance the solver method between the Maxwell and Transport equation.