Original article

Numerische Mathematik

, Volume 86, Issue 4, pp 635-654

First online:

Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval

  • Ben-Yu GuoAffiliated withDepartment of Mathematics, Shanghai Normal University, Shanghai, 200234, China
  • , Jie ShenAffiliated withDepartment of Mathematics, Penn State University, University Park, PA16802, USA

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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.

Mathematics Subject Classification (1991): 65N35, 65N22, 65F05, 35J05