Blow-up phenomena in the model of a space charge stratification in semiconductors: numerical analysis of original equation reduction to a differential-algebraic system

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.