Comparative analysis by means of finite differences and DM methods for linearized problem of gyrotrons

Abstract

The problem of Schrödinger equation with complex boundary conditions for modelling a motion of electrons in gyrotrons is considered. Numerical results obtained by using Fourier, Finite Differences (FD) and Degenerate Matrices (DM) methods are compared in the simplest case. For DM methods they are analysed also in more general cases, when FD can not be applied because of fast oscillations of the solution.

Nagrinejamas kraštinis uždavinys Šredingerio lygčiai, aprašantis elektronu judejima girotrone. Darbe lyginami ir analizuojami Furje, baigtiniu skirtumu ir degeneruotu matricu (DM) metodais gauti skaitiniai rezultatai. Aptartas metodo taikymas greitu osciliaciju atveju.

Key words:

• gyrotron
• Schrödinger equation
• complex boundary conditions
• Fourier method
• finite differences
• degenerate matrices method