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 Num. Meth. Prog., 2016, Volume 17, Issue 4, Pages 437–446 (Mi vmp849)

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

D. V. Luk'yanenko, A. A. Panin

Faculty of Physics, Lomonosov Moscow State University

Abstract: 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.

Full text: PDF file (348 kB)
UDC: 519.6

Citation: 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”, Num. Meth. Prog., 17:4 (2016), 437–446

Citation in format AMSBIB
\Bibitem{LukPan16} \by D.~V.~Luk'yanenko, A.~A.~Panin \paper Blow-up phenomena in the model of a space charge stratification in semiconductors: numerical analysis of original equation reduction to a differential-algebraic system \jour Num. Meth. Prog. \yr 2016 \vol 17 \issue 4 \pages 437--446 \mathnet{http://mi.mathnet.ru/vmp849} 

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• http://mi.mathnet.ru/eng/vmp/v17/i4/p437

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This publication is cited in the following articles:
1. I. I. Kolotov, A. A. Panin, “On Nonextendable Solutions and Blow-Ups of Solutions of Pseudoparabolic Equations with Coercive and Constant-Sign Nonlinearities: Analytical and Numerical Study”, Math. Notes, 105:5 (2019), 694–706
2. M. O. Korpusov, A. K. Matveeva, D. V. Lukyanenko, “Diagnostika mgnovennogo razrusheniya resheniya v nelineinom uravnenii teorii voln v poluprovodnikakh”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:4 (2019), 104–113
3. A. A. Panin, G. I. Shlyapugin, “Local Solvability and Global Unsolvability of a Model of Ion-Sound Waves in a Plasma”, Math. Notes, 107:3 (2020), 464–477
4. M. O. Korpusov, E. A. Ovsyannikov, “Blow-up instability in non-linear wave models with distributed parameters”, Izv. Math., 84:3 (2020), 449–501
5. M. O. Korpusov, “Blow-up and global solubility in the classical sense of the Cauchy problem for a formally hyperbolic equation with a non-coercive source”, Izv. Math., 84:5 (2020), 930–959