Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations

Leaders of the field break down global spectral methods for fractional differential equations, a new frontier of mathematical modeling.

Mohsen Zayernouri (Author), Li-Lian Wang (Author), Jie Shen (Author), George Em Karniadakis (Author)

9781108490993, Cambridge University Press

Hardback, published 14 November 2024

742 pages
23.6 x 16.1 x 4.3 cm, 1.16 kg

'It should be a valuable reference for researchers and advanced graduate students in numerical analysis, scientific computing, and fractional differential equations.' Chang-Tao Sheng, MathSciNet

This comprehensive introduction to global spectral methods for fractional differential equations from leaders of this emerging field is designed to be accessible to graduate students and researchers across math, science, and engineering. The book begins by covering the foundational fractional calculus concepts needed to understand and model anomalous transport phenomena. The authors proceed to introduce a series of new spectral theories and new families of orthogonal and log orthogonal functions, then present corresponding spectral and spectral element methods for fractional differential equations. The book also covers the fractional Laplacian in unbounded and bounded domains and major developments in time-integration of fractional models. It ends by sampling the wide variety of real-world applications of fractional modeling, including concentration transport in surface/subsurface dynamics, complex rheology and material damage, and fluid turbulence and geostrophic transport.

1. Fractional calculus and anomalous transport
2. Spectral expansions and related approximations
3. Global schemes for fractional ODEs (FODEs)
4. Global schemes for fractional PDEs (FPDEs)
5. Integral fractional Laplacian in unbounded domains
6. Fractional Laplacian in bounded domains
7. Time-integration of fractional models
8. Applications of anomalous transport and fractional modeling
References
Index.

Subject Areas: Numerical analysis [PBKS]