Stokes first problem for a Newtonian fluid in a non-Darcian porous half-space using a Laguerre-Galerkin method

A Laguerre-Galerkin method is proposed and analysed for the Stokesʹ first problem of a Newtonian fluid in a non-Darcian porous halfspace on a semi-infinite interval. It is well known that Stokesʹ first problem has a jump discontinuity on boundary which is the main obstacle in numerical methods. 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 of the transformed equations is developed and implemented. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented.