Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations

We construct two variable-step linearly implicit Runge-Kutta methods of ord ers 3 and 4 for the numerical integration of the semidiscrete equations ari sing after the spatial discretization of advection-reaction-diffusion equat ions. We study the stability properties of these methods giving the appropr iate extension of the concept of L-stability. Numerical results are reporte d when the methods presented are combined with spectral discretizations. Ou r experiments show that the methods, being easily implementable, can be com petitive with standard stiffly accurate time integrators. (C) 2001 IMACS. P ublished by Elsevier Science B.V. All rights reserved.