Convergence of the Peaceman-Rachford approximation for reaction-diffusion systems

Consider a reaction-diffusion system of the form u(t)-MDeltau+F(u)=0, where M is a mxm matrix whose spectrum is included in {Rz>0}. We approximate it by the Peaceman-Rachford approximation defined by P(t)=(1+tF/2)(-1)(1+tMDelta/2)(1-tMDelta/2)(-1)(1-tF/2). We prove convergence of this scheme and show that it is of order two.