Laguerre spectral approximation of Stokes' first problem for third-grade fluid

Abstract

A Laguerre-Galerkin method is proposed and analyzed for Quasilinear parabolic differential equation which arises from Stokes' first problem for a third-grade fluid on a semi-infinite interval. By reformulating this equation 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. Effects of non-Newtonian parameters on the flow phenomena are analyzed and documented. (C) 2007 Elsevier Ltd. All rights reserved.