Second-order methods for diffusion-convection equations

The method of lines provides a flexible and general approach for solving time-dependent PDEs. However, the numerical solution of the resulting ODE system can present certain difficulties depending on the method used. In particular, oscillations may appear in the solution when standard methods are applied to the ODE system arising from the semi-discretization of the diffusion-convection equation partial derivative u/partial derivative t = partial derivative(partial derivative(2)u/partial derivative x(2)) -beta(partial derivative u/partial derivative x). We examine second-order methods for such systems and present economical L-stable predictor-corrector schemes which are oscillation-free. Copyright (C) 1999 John Wiley & Sons, Ltd.