(Massey University, 2006) Thongmoon, M.; McKibbin, R.
This paper describes a comparison of some numerical methods for solving the
advection-diffusion (AD) equation which may be used to describe transport
of a pollutant. The one-dimensional advection-diffusion equation is solved by
using cubic splines (the natural cubic spline and a ”special” AD cubic spline)
to estimate first and second derivatives, and also by solving the same problem
using two standard finite difference schemes (the FTCS and Crank-Nicolson
methods). Two examples are used for comparison; the numerical results are
compared with analytical solutions. It is found that, for the examples studied,
the finite difference methods give better point-wise solutions than the spline
methods.
