Chocholatý, Pavol
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Reaction-diffusion equations arise as mathematical models in a series of important applications. Some difference schemes to the solution of the Fisher's equation are presented.
Guo Ben Yu, A.R. Mitchell (1986)
Numerische Mathematik
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Claire Chainais-Hillairet, Jian-Guo Liu, Yue-Jun Peng (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We introduce a finite volume scheme for multi-dimensional drift-diffusion equations. Such equations arise from the theory of semiconductors and are composed of two continuity equations coupled with a Poisson equation. In the case that the continuity equations are non degenerate, we prove the convergence of the scheme and then the existence of solutions to the problem. The key point of the proof relies on the construction of an approximate gradient of the electric potential which allows...