A Second-order Space and Time Nodal Method for the One-dimensional Convection-diffusion Equation

Abstract---We present a nodal integral method for the one-dimensional convection-diffusion equation. The development is carried out in the nodal spirit, and results in a method that is second order both in space and time variables. Extension of this method, which is characterized by inherent upwinding, to multi-dimensional problems is straightforward. The nodal method’s ability to yield accurate results on rather coarse mesh sizes when coupled with node interior reconstruction of the solution results in a rather powerful r;cheme that can accurately resolve the solution--even in regions with sharp gradients-with relatively large node sizes. Three widely used problems are solved numerically to demonstrate the properties of the nodal method developed here.