Name
Title | ||
|---|---|---|
Generalized Hermite Approximations and Spectral Method for Partial Differential Equations in Multiple Dimensions |
Abstract | ||
|---|---|---|
In this paper, we consider a spectral method based on generalized Hermite functions in multiple dimensions. We first introduce three normed spaces and prove their equivalence, which enables us to develop and to analyze generalized Hermite approximations efficiently. We then establish some basic results on generalized Hermite orthogonal approximations in multiple dimensions, which play important roles in the relevant spectral methods. As examples, we consider an elliptic equation with a harmonic potential and a class of nonlinear wave equations. The spectral schemes are proposed, and the convergence is proved. Numerical results demonstrate the spectral accuracy of this approach. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s10915-013-9703-2 | J. Sci. Comput. |
Keywords | Field | DocType |
spectral accuracy,relevant spectral method,spectral method,harmonic potential,generalized hermite orthogonal approximation,basic result,partial differential equations,multiple dimensions,elliptic equation,generalized hermite approximations,multiple dimension,spectral scheme,generalized hermite function | Convergence (routing),Mathematical optimization,Hermite spline,Mathematical analysis,Hermite polynomials,Equivalence (measure theory),Spectral method,Partial differential equation,Hermite interpolation,Elliptic curve,Mathematics | Journal |
Volume | Issue | ISSN |
57 | 2 | 1573-7691 |
Citations | PageRank | References |
4 | 0.46 | 11 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xin-min Xiang | 1 | 17 | 1.71 |
| Zhong-qing Wang | 2 | 140 | 20.28 |