Linearly implicit Runge–Kutta methods for advection–reaction–diffusion equations Original Research Article

We construct two variable-step linearly implicit Runge–Kutta methods of orders 3 and 4 for the numerical integration of the semidiscrete equations arising after the spatial discretization of advection–reaction–diffusion equations. We study the stability properties of these methods giving the appropriate extension of the concept of L-stability. Numerical results are reported when the methods presented are combined with spectral discretizations. Our experiments show that the methods, being easily implementable, can be competitive with standard stiffly accurate time integrators.