"A study of self-oscillation instability in varicap-based electrical networks: analytical and numerical approaches"
Vasilchenko V.A., Korpusov M.O., Lukyanenko D.V., and Panin A.A.

The blow-up of solutions is analytically and numerically studied for a certain Sobolev-type equation describing processes in varicap-based electrical networks. The energy method is used for the analytical study. For the numerical analysis, the original partial differential equation is approximated using a system of ordinary differential equations solved by the one-stage Rosenbrock scheme with a complex coefficient. The numerical diagnostics of solution's blow-up is based on a posteriori asymptotically exact error estimation on sequentially condensed grids.

Keywords: Sobolev-type equation, numerical diagnostics of solution's blow-up.

  • Vasilchenko V.A. – Lomonosov Moscow State University, Faculty of Physics; Leninskie Gory, Moscow, 119991, Russia; Student, e-mail: v.v.a.onside@gmail.com
  • Korpusov M.O. – Lomonosov Moscow State University, Faculty of Physics; Leninskie Gory, Moscow, 119991, Russia; Dr. Sci., Professor, e-mail: korpusov@gmail.com
  • Lukyanenko D.V. – Lomonosov Moscow State University, Faculty of Physics; Leninskie Gory, Moscow, 119991, Russia; Ph.D., Associate Professor, e-mail: lukyanenko@physics.msu.ru
  • Panin A.A. – Lomonosov Moscow State University, Faculty of Physics; Leninskie Gory, Moscow, 119991, Russia; Ph.D., Associate Professor, e-mail: a-panin@yandex.ru