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

Abstract

Summary.A Laguerre-Galerkin method is proposed and analyzed for the Burgers equation and Benjamin-Bona-Mahony (BBM) equation on a semiinfinite 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. Classification (1991): 65N35, 65N22, 65F05, 35J05 Mathematics Subject

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