Implicit factorization techniques for two-dimensional, anisotropic, reactive-diffusive media with cross-diffusion effects

The propagation of fronts in two–dimensional, anisotropic, nonlinear reactive–diffusive media with cross–diffusion is analyzed by means of implicit time–linearized factorization techniques. Four factorization methods are considered; the first one disregards the approximate factorization errors and treats the mixed second–order derivatives explicitly, whereas the other three account for either the approximate factorization errors or the mixed second–order derivative terms in an iterative manner. The four techniques involve the solution of one–dimensional operators and require the solution of linear algebraic systems with block–tridiagonal matrices. It is shown that anisotropy and cross–diffusion deform the reaction front and affect the front velocity. It is also shown that the approximate factorization method that treats the mixed second–order derivative terms iteratively provide much more accurate transient results than techniques that account for the approximate factorization errors and treat the mixed s...