Spectral method for multi-dimensional problems of high order on unbounded domains using generalized Laguerre functions

Abstract

More and more attention has been paid to numerical methods for problems on unbounded domains. In this paper, a spectral method using generalized Laguerre functions is proposed for high dimensional problems of high order defined on unbounded domains. The new basis is introduced, and some orthogonal and interpolation approximation results are established, which serve as useful tools in spectral methods for high order problems. As examples of applications, the spectral schemes for the fourth order problems are presented. Efficient algorithms are implemented. The numerical results are shown to demonstrate the high accuracy of suggested algorithms, which are coincided with the theoretical analysis.