Pseudospectral Method Using Generalized Laguerre Functions And Its Applications

Many problems in science and engineering are set in unbounded domains. The simplest method to deal with them is to set some artificial boundaries, impose certain artificial boundary conditions and then resolve them numerically. Whereas these treatments may cause additional errors. Thereby, it seems better to solve such problems directly.In this dissertation, we develop the pseudospectral method for differential equations defined on unbounded domains. We first introduce the Gauss-type interpolations using a new family of generalized Laguerre functions, and establish the basic approximation results. Then we propose the pseudospectral method for differential equations on unbounded domains, whose coefficients may degenerate or grow up. As examples. we consider two model problems. The proposed schemes match the underlying problems properly and possess the spectral accuracy. Numerical results demonstrate the efficiency of this new approach.