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

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

• Gebundenes Buch

Produktbeschreibung

Fractional modeling is a new frontier of high-fidelity predictive modeling approaches in mathematics, science, and engineering. This introduction for graduate students and researchers is a guide to numerically solving fractional differential equations as tractable models for complex rheology, aging materials, and turbulence.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 734
• Erscheinungstermin: 30. September 2024
• Englisch
• ISBN-13: 9781108490993
• ISBN-10: 1108490999
• Artikelnr.: 70602329

Autorenporträt

Mohsen Zayernouri is Associate Professor of Mechanical Engineering and Statistics and Probability at Michigan State University. He is the recipient of two Young Investigator Program (YIP) awards from the US Air Force Office of Scientific Research (AFOSR) and Army Research Office (ARO). He brings to bear advanced computational tools from applied mathematics and data sciences to develop stochastic modeling and predictive simulation tools for challenging physical and engineering problems, including: stochastic Lévy processes in turbulent flows and anomalous transport in multi-scale and disordered bio-materials.

Inhaltsangabe

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.