Finite Difference Methods for Fractional Diffusion Equations

The book "Finite Difference Methods for Fractional Diffusion Equations" offers a comprehensive introduction to finite difference methods for time-dependent, space-fractional diffusion equations. It places particular emphasis on the theoretical properties and the practical computer-based implementation of these methods. The content is presented within a coherent framework that unifies previously scattered results from the literature. In addition to addressing numerical methods for fractional diffusion equations and their exact solutions, the connection to Lévy flights is also explained. The book furthermore provides an accessible overview of fundamental concepts related to Riemann–Liouville fractional derivatives. The final chapters are devoted to scenarios with boundary conditions, thereby filling a gap in the existing literature. Each chapter includes exercises that deepen understanding and prepare readers for further specialized studies. Written from the perspective of a mathematician with a passion for physics and computation, the work is aimed at researchers who wish to delve into this exciting topic, and it appeals to both graduates and experts from various fields who wish to engage with mathematical, physical, and computer-based ideas.