Legendre-Laguerre coupled spectral element methods for second- and fourth-order equations on the half line

Authors:
Qingqu Zhuang;Chuanju Xu
Affiliations:
School of Mathematical Sciences, Huaqiao University, 362021 Quanzhou, China;School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

Some Legendre spectral element/Laguerre spectral coupled methods are proposed to numerically solve second- and fourth-order equations on the half line. The proposed methods are based on splitting the infinite domain into two parts, then using the Legendre spectral element method in the finite subdomain and Laguerre method in the infinite subdomain. C^0 or C^1-continuity, according to the problem under consideration, is imposed to couple the two methods. Rigorous error analysis is carried out to establish the convergence of the method. More importantly, an efficient computational process is introduced to solve the discrete system. Several numerical examples are provided to confirm the theoretical results and the efficiency of the method.