Geodesic
Blow-up phenomena in the model of a space charge stratification in semiconductors: numerical analysis of original equation reduction to a differential-algebraic system
Numerical methods and programming, Tome 17 (2016) no. 4, pp. 437-446.

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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. 
@article{VMP_2016_17_4_a7,
     author = {D. V. Luk'yanenko and A. A. Panin},
     title = {Blow-up phenomena in the model of a space charge stratification in semiconductors: numerical analysis of original equation reduction to a differential-algebraic system},
     journal = {Numerical methods and programming},
     pages = {437--446},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2016_17_4_a7/}
}
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D. V. Luk'yanenko; A. A. Panin. Blow-up phenomena in the model of a space charge stratification in semiconductors: numerical analysis of original equation reduction to a differential-algebraic system. Numerical methods and programming, Tome 17 (2016) no. 4, pp. 437-446. http://geodesic.mathdoc.fr/item/VMP_2016_17_4_a7/