Entropy decay of discretized fokker-planck equations I—Temporal semidiscretization
| Autor: | Andreas Unterreiter, Anton Arnold |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
Exponential decay rate
Kullback–Leibler divergence Relative entropy Logarithm Discretization Logarithmic Sobolev inequality Mathematical analysis Fokker-Planck equation Sobolev inequality Computational Mathematics Exponential growth Computational Theory and Mathematics Modeling and Simulation Modelling and Simulation Fokker–Planck equation Exponential decay Entropy (arrow of time) Mathematics |
| Zdroj: | Computers & Mathematics with Applications. 46(10-11):1683-1690 |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/s0898-1221(03)90202-1 |
| Popis: | In this paper, we study the large time behavior of a fully implicit semidiscretization (in time) of parabolic Fokker-Planck type equations. Using logarithmic Sobolev inequalities exponential decay of the relative entropy (w.r.t. the steady state) is proved which yields convergence of the discrete scheme towards the unique steady state. The exponential decay rate recovers as At J 0 the decay rate of the original Fokker-Planck type equations. |
| Databáze: | OpenAIRE |
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