Spectral and pseudospectral approximations using Hermite functions: Application to the Dirac equation. (English) Zbl 1032.33004

Guo, Ben-yu; Shen, Jie; Xu, Cheng-long

Adv. Comput. Math. 19, No. 1-3, 35-55 (2003).

Summary: There are used Hermite functions for PDEs on the whole line for construction of spectral and pseudospectral approximation. By this method there is approximated the Dirac equation. Particularly, these methods preserve the essential conservation property of the Dirac equation. Some numerical results illustrate the effectiveness of these methods.

Reviewer: J.Kofroň (Praha)

MSC:

33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
41A10	Approximation by polynomials
65N35	Spectral, collocation and related methods for boundary value problems involving PDEs

Keywords:

Hermite approximation; Dirac equation; spectral and pseudospectral