Advection-diffusion Equations: Temporal Sinc Methods

A fully Sinc-Galerkin method for solving advection-di usion equations subject to arbitrary radiation boundary conditions is presented. This procedure gives rise to a discretization which has it's most natural representation in the form of a Sylvester system where the coe cient matrix for the temporal discretization is full. The word \full" often implies a computationally more complex method compared to, for example, temporal marching. In a comparison of time-marching versus this sinc-temporal procedure, the Sylvester formulation de nes a common framework within which these procedures can be evaluated. This framework has been included in the introduction to illustrate an e ciency measure for either method. Similar remarks with regard to fullness versus sparseness in the Sylvester formulation apply when the spatial discretization is spectral or, for example di erencing. Although it is indicated how this sinc-temporal method can be combined with alternative spatial discretizations, the natural a nity between sinc methods for space and time discretizations motivate carrying out the numerical illustrations using the sinc base in each. i