Some Recent Advances on Spectral Methods for Unbounded Domains

By Jie Shen, Lilian Wang. Communications in Computational Physics, 2009

181 citations recorded by the source corpus.

We present in this paper a unified framework for analyzing the spectral methods in unbounded domains using mapped Jacobi, Laguerre and Hermite functions. A detailed comparison of the convergence rates of these spectral methods for solutions with typical decay behaviors is carried out, both theoretically and computationally. A brief review on some of the recent advances in the spectral methods for unbounded domains is also presented. AMS subject classifications: 65N35, 65N22,65F05, 35J05

Subfields: Mathematical Physics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c089d677a5f481e4b899a71eb9d48646a00da5d8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Ali H. Bhrawy
2. Dumitru Băleanu
3. LM Assas

In Modeling and Simulation

1. Dumitru Băleanu
2. Ali H. Bhrawy
3. LM Assas
4. M. A. Zaky
5. Amin Jajarmi
6. Thabet Abdeljawad
7. Arran Fernandez
8. Xiao-jun Yang

In Numerical Analysis

1. Dumitru Băleanu
2. Ali H. Bhrawy
3. LM Assas
4. Arran Fernandez
5. Amin Jajarmi
6. Thabet Abdeljawad
7. M. A. Zaky
8. Pshtiwan Othman Mohammed

Citations in the corpus

• Efficient generalized Laguerre-spectral methods for solving multi-term fractional differential equations on the half line (2014, methodology): “For problems with decay at infinity, it is convenient to use the generalized Laguerre functions (see Guo et al., 2006; Shen and Wang, 2009).”