  Linearly implicit Runge-Kutta methods with approximate matrix factorization
can solve efficiently large systems of differential equations that have a stiff
linear part, e.g. reaction-diffusion systems. However, the use of approximate
factorization usually leads to loss of accuracy, which makes it attractive only
for low order time integration schemes. This paper discusses the application of
approximate matrix factorization with high order methods; an inexpensive
correction procedure applied to each stage allows to retain the high order of
the underlying linearly implicit Runge-Kutta scheme. The accuracy and stability
of the methods are studied. Numerical experiments on reaction-diffusion type
problems of different sizes and with different degrees of stiffness illustrate
the efficiency of the proposed approach.
