Glenn R. Ierley, Department of Mathematical Sciences, Michigan Technological University, Houghton Michigan 49931
Brian Spencer, Department of Engineering Science and Applied Mathematics, Northwestern University, Evanston, IL 60201
Rodney Worthing, Department of Mathematics, MIT, Cambridge, MA 02139 ABSTRACT:In this paper, we introduce a fully spectral solution for the partial differential equation: u_t + u u_x + nu u_xx + mu u_xxx + lambda u_xxxx = 0. For periodic boundary conditions in space, the use of a Fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a Chebyshev series. Boundary conditions other than periodic may still be treated with reasonable, though lesser, efficiency. For all cases, very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time.