Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval |
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| Authors: | Ben-Yu Guo and Jie Shen |
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| Affiliation: | (1) Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China , CN;(2) Department of Mathematics, Penn State University, University Park, PA16802, USA , US |
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| Abstract: | Summary. A Laguerre-Galerkin method is proposed and analyzed for the Burgers equation and Benjamin-Bona-Mahony (BBM) equation on a semi-infinite interval. By reformulating these equations with suitable functional transforms, it is shown that the Laguerre-Galerkin approximations are convergent on a semi-infinite interval with spectral accuracy. An efficient and accurate algorithm based on the Laguerre-Galerkin approximations to the transformed equations is developed and implemented. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. Received October 6, 1997 / Revised version received July 22, 1999 / Published online June 21, 2000 |
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| Keywords: | Mathematics Subject Classification (1991): 65N35 65N22 65F05 35J05 |
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