Pseudospectral method using generalized Laguerre functions for singular problems on unbounded domains

Spherical harmonic-generalized Laguerre pseudospectral method for three-dimensional exterior problems

“…According to Theorem 3.2 in [21], if |v| A r α−1,β , and |v| A r α,β , are finite with integer r > 1 and r > α + 1, then…”

“…The mathematical foundation of mixed pseudospectral method for three-dimensional exterior problems with a ball obstacle is the mixed spherical harmonic-generalized Laguerre interpolation. Wang et al [21] developed the generalized Laguerre interpolation, while Cao and Guo [2] investigated the interpolation on the spherical surface, also see Swarztrauber [20]. The related approximation results in [2,21] produce the possibility of designing a large class of reasonable mixed pseudospectral methods for three-dimensional unbounded domains.…”

“…Wang et al [21] developed the generalized Laguerre interpolation, while Cao and Guo [2] investigated the interpolation on the spherical surface, also see Swarztrauber [20]. The related approximation results in [2,21] produce the possibility of designing a large class of reasonable mixed pseudospectral methods for three-dimensional unbounded domains. This paper is devoted to the mixed pseudospectral method for three-dimensional exterior problem with a ball obstacle.…”

Linearly Time Efficiency in Unattended Wireless Sensor Networks

“…Laguerre-Gauss-Radau points and generalized Laguerre-Gauss-type interpolation were introduced by [24,[28][29][30].…”

Mixed Spectral and Pseudospectral Methods for a Nonlinear Strongly Damped Wave Equation in an Exterior Domain

“…The generalized Laguerre functions are very suitable for numerical simulation of various problems in exterior domains. For instance, Wang, Guo and Wu [16] developed a pseudospectral method for symmetric solutions of partial differential equations outside a disc, by using the generalized Laguerre functions (1.2). Meanwhile, Wang, Guo and Zhang [17] proposed a mixed spectral method for three-dimensional exterior problems using spherical harmonic and generalized Laguerre functions.…”