Abstract
In this paper, we develop the mixed spectral and pseudospectral methods for two-dimensional exterior problems, by using the scaled generalized Laguerre functions. Some basic results on the mixed Fourier-Laguerre orthogonal approximation and Gauss-type interpolation are established, which play important roles in the related spectral and pseudospectral methods. As an example, we propose the mixed spectral and pseudospectral schemes for a model problem. The convergence of proposed schemes are proved. Numerical results demonstrate the spectral accuracy efficiency of this new approach.
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This work is supported in part by NSF of China, N.10771142, the National Basic Research Project N.2005CB321701, SF of Shanghai N.075105118, The Shanghai Leading Academic Discipline Project N.T0401 and The Fund for E-institute of Shanghai Universities N.E03004.
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Zhang, R., Wang, Zq. & Guo, By. Mixed Fourier-Laguerre Spectral and Pseudospectral Methods for Exterior Problems Using Generalized Laguerre Functions. J Sci Comput 36, 263–283 (2008). https://doi.org/10.1007/s10915-008-9189-5
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DOI: https://doi.org/10.1007/s10915-008-9189-5