Log orthogonal functions: approximation properties and applications
Abstract
We present two new classes of orthogonal functions, log orthogonal functions and generalized log orthogonal functions, which are constructed by applying a $\log $ mapping to Laguerre polynomials. We develop basic approximation theory for these new orthogonal functions, and apply them to solve several typical fractional differential equations whose solutions exhibit weak singularities. Our error analysis and numerical results show that our methods based on the new orthogonal functions are particularly suitable for functions that have weak singularities at one endpoint and can lead to exponential convergence rate, as opposed to low algebraic rates if usual orthogonal polynomials are used.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 23, 2020
- Source ID
- 10.1093/imanum/draa087
Entities
People
- Jie Shen
- Sheng Chen
Organizations
- Air Force Office of Scientific Research
- China Postdoctoral Science Foundation
- Jiangsu Normal University
- National Natural Science Foundation of China
- Purdue University