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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received October 6, 1997 / Revised version received July 22, 1999 / Published online June 21, 2000
Rights and permissions
About this article
Cite this article
Guo, BY., Shen, J. Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval. Numer. Math. 86, 635–654 (2000). https://doi.org/10.1007/PL00005413
Issue Date:
DOI: https://doi.org/10.1007/PL00005413