Abstract
In this chapter, we present a selection of results from our fund of numerical experiments. We methodically focus on the approach based upon the numerical solution of the system (3.17) of nonlinear Hammerstein integral equations, as described in Chaps. 3 and 6. The finite element method from Chap. 5 has also been implemented and successfully tested (Angermann, Yatsyk, Int J Electromagn Waves Electron Syst 13(12), 15–30, 2008, [1]) (Hoff, Numerische Simulation der Oberwellengeneration in nichtlinearen elektromagnetischen Diffraktionsproblemen. Diploma thesis (supervisor: L. Angermann), Department of Mathematics, Clausthal University of Technology, 2014, [2]). Since the obtained approximations to the solution of the boundary value problem (1.66) were largely comparable to the numerical results for the system (3.17) and thus did not provide any other (or even new) findings, we have omitted a similarly detailed description and discussion of the finite element results. Nevertheless, we have included a few comments on these results.
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- 1.
Since there is no danger of confusion, here and in what follows, we will not make a notational difference between \(\varepsilon _{n\kappa }=\varepsilon _{n\kappa }(z,\alpha (z),U(z,\kappa ),U(z,2\kappa ),U(z,3\kappa ))\) and \(\varepsilon _{n\kappa }=\varepsilon _{n\kappa }(z,\alpha (z),U(z,\kappa ),U(z,3\kappa ))\).
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Angermann, L., Yatsyk, V.V. (2019). Numerical Experiments. In: Resonant Scattering and Generation of Waves. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-96301-3_7
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DOI: https://doi.org/10.1007/978-3-319-96301-3_7
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