Finite Difference Methods for Fractional Diffusion Equations : One-Dimensional Time-Dependent Problems / by Ercília Sousa.

Format:

Book

Author/Creator:

Sousa, Ercília.

Series:

Lecture Notes in Mathematics, 1617-9692 ; 2389

Language:

English

Subjects (All):

Differential equations.

Numerical analysis.

Differential Equations.

Numerical Analysis.

Local Subjects:

Differential Equations.

Numerical Analysis.

Physical Description:

1 online resource (314 pages)

Edition:

1st ed. 2026.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2026.

Summary:

This book provides a self-contained introduction to finite difference methods for time-dependent space-fractional diffusion equations, emphasizing their theoretical properties and practical computational implementation. It collects results previously dispersed throughout the literature, presenting them within a coherent unified framework. In addition to covering numerical methods for fractional diffusion equations, their exact solutions, and their connection to Lévy flights, it also offers an accessible overview of fundamental concepts related to Riemann–Liouville fractional derivatives. By presenting a comprehensive treatment of the fundamental techniques of finite difference methods, the book lays a solid foundation for mastering the intricacies of finite differences for fractional differential equations. The final chapters address scenarios with boundary conditions, filling a gap in the existing literature. Each chapter concludes with exercises designed to help deepen the reader’s understanding and prepare them for further specialized study. Written from the perspective of a mathematician who enjoys physics and computation, the volume is intended as a starting point for any researcher who wants to enter into this exciting subject. It will appeal to graduate students and experts from different backgrounds who enjoy digging into mathematical, physical and computational ideas.

Contents:

Prelude

Fractional derivatives: fundamental concepts

A governing equation for Lévy flights

Consistency, stability and convergence of numerical methods

Fractional differential equations in unbounded domains

Fractional differential equations in bounded domains: absorbing boundaries

Fractional differential equations in bounded domains: reflecting boundaries

The road ahead

References.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-032-11222-2

9783032112224

OCLC:

1568045664