A New Generalized Laguerre Function-Generalized Hermite Function Mixed Approximation and its Application to Nonlinear Differential Equation
Abstract
The generalized Laguerre-generalized Hermite mixed spectral method is developed. Various orthogonal projections are investigated. Some mixed approximation results are established. As an example of their important applications, a mixed spectral scheme is proposed for a two-dimensional nonlinear problem. Its convergence is proved. Numerical results demonstrate the high accuracy of this new spectral method.
- Publication:
-
Computational Methods in Science and Engineering: Advances in Computational Science: Lectures presented at the International Conference on Computational Methods in Sciences and Engineering 2008 (ICCMSE 2008)
- Pub Date:
- August 2009
- DOI:
- 10.1063/1.3225450
- Bibcode:
- 2009AIPC.1148..851X
- Keywords:
-
- 44.05.+e;
- 02.60.Cb;
- 41.20.Cv;
- 02.30.Jr;
- Analytical and numerical techniques;
- Numerical simulation;
- solution of equations;
- Electrostatics;
- Poisson and Laplace equations boundary-value problems;
- Partial differential equations