Attaining exponential convergence for the flux error with second- and fourth-order accurate finite-difference...

This article demonstrates that exponential convergence of the flux error can be achieved for any kinetic-diffusion system comprising an arbitrary number of (pseudo) first-order chemical reactions if the underlying PDEs are discretized as outlined for the box 2 or box 4 method in the preceding part of this article. By investigating the eigenvalues and eigenvectors of the first-order kinetic coupling matrix in general form the present article demonstrates that the simulation of any multispecies first-order kinetic diffusion system can be as accurately done as the simulation of a single representative one-species system. The Fourier coefficients governing the error level of the flux are much smaller in the limiting case of kinetic control as those reported in the preceding article for the limiting case of diffusion control. The higher rate of exponential convergence predicted on the basis of the mathematical model has been fully verified by the numerical results.