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Deng W., Zhang Z. High Accuracy Algorithm for the Differential Equations Governing Anomalous Diffusion: Algorithm and Models for Anomalous Diffusion

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Deng W., Zhang Z. High Accuracy Algorithm for the Differential Equations Governing Anomalous Diffusion: Algorithm and Models for Anomalous Diffusion
World Scientific Publishing, 2019. — 295 p. — ISBN 9813142200.
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.
Contents
Introduction
Mathematical models
Numerical methods for the time fractional differential equations
High order finite difference methods for the space fractional PDEs
Variational numerical method for the space fractional PDEs
Appendixes
Basic concepts for functional and numerical analysis
Some properties of the fractional calculus
Iteration methods for linear systems generated from fractional PDEs
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