Survey of Numerical Methods for Fractional Differential Equations for Directed Energy Applications
Abstract
Nonlocal operators of the fractional calculus have demonstrated the ability to model physical phenomena that have been shown to be problematic for models based on traditional integer-order calculus. Though these models based on the fractional calculus can produce highly accurate results, they come with the price of increased complexity and high computational cost. In some cases, the increased level of complexity is so high that numerical methods are sometimes necessary to implement even though an analytical solution for the problem may exist, making the importance of numerical methods for solving fractional differential equations more pronounced than perhaps even their integer ordercounterparts. In this survey, numerical methods popular with the fractional calculus community have been gathered, coded, and scrutinized for practical use in the multidisciplinary field of directed energy. Numerical methods stemming from basic definitions of fractional derivatives, methods based on predictor-corrector algorithms, and matrix methods in the context of fractional partial differential equations for viscoelastic, diffusion, and heating problems are considered.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 18, 2021
- Accession Number
- AD1142398
Entities
People
- Andrew. W. Wharmby
- Victor M. Chen
Organizations
- 711th Human Performance Wing
- Oak Ridge Institute for Science and Education