High Accuracy Algorithm For The Differential Equations Governing Anomalous Diffusion: Algorithm And Models For Anomalous Diffusion

The aim of this book is to extend the application field of 'anomalous diffusion', and describe the newly built models and the simulation techniques to the models.The book first introduces 'anomalous diffusion' from the statistical physics point of view, then discusses the models characterizing anomalous diffusion and its applications, including the Fokker-Planck equation, the Feymann-Kac equations describing the functional distribution of the anomalous trajectories of the particles, and also the microscopic model — Langevin type equation. The second main part focuses on providing the high accuracy schemes for these kinds of models, and the corresponding convergence and stability analysis.

Scopul acestei carti este de a extinde campul de aplicare al „difuziei anormale” si de a descrie modelele nou construite si tehnicile de simulare la modele. Cartea introduce mai intai „difuziunea anomala” din punctul de vedere al fizicii statistice, apoi discuta despre modele care caracterizeaza difuzia anomala si aplicatiile sale, inclusiv ecuatia Fokker-Planck, ecuatiile Feymann-Kac care descriu distributia functionala a traiectoriilor anormale ale particulelor, precum si modelul microscopic - ecuatia de tip Langevin.