A comparison of some numerical methods for the advection-diffusion equation
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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.
Thongmoon, M., McKibbin, R. (2006), A comparison of some numerical methods for the advection-diffusion equation, Research Letters in the Information and Mathematical Sciences, 10, 49-62