A study of self-oscillation instability in varicap-based electrical networks: analytical and numerical approaches

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 solutions blow-up is based on a posteriori asymptotically exact error estimation on sequentially condensed grids.