"Blow-up phenomena in the model of a space charge stratification in semiconductors: numerical analysis of original equation reduction to a differential-algebraic system"
Luk'yanenko D.V. and Panin A.A.

The efficiency of one of the methods for the numerical diagnostics of solution's blow-up is shown using the example of solving a nonlinear Sobolev-type equation that describes a space charge stratification in semiconductors. An approach to reduce the original partial differential equation to a differential-algebraic system is used. This system is solved by the Rosenbrock scheme with a complex coefficient. The numerical diagnostics of solution's blow-up is based on the Richardson extrapolation procedure.

Keywords: numerical diagnostics of solution's blow-up, Rosenbrock method, partial differential equations, differential-algebraic equations.

  • Luk'yanenko 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