AbstractThis is an attempt to construct a strong numerical method for transportdiffusion
equations with nonlinear reaction terms, which relies on the idea of the Modified
Method of Characteristics that is explicit but stable and is second-order accurate
in time. The method consists in convective-diffusive splitting of the equations along
the characteristics. The convective stage of the splitting is straightforwardly treated
by a quasi-monotone and conservative modified method of characteristics, while the
diffusive-reactive stage can be approximated by an explicit scheme with an extended
real stability interval. A numerical comparative study of the new method with Characteristics
Crank-Nicholson and Classical Characteristics Runge-Kutta schemes, which
are used in many transport-diffusion models, is carried out for several benchmark problems,
whose solutions represent relevant transport-diffusion-reaction features.
Experiments for transport-diffusion equations with linear and nonlinear reactive sources
demonstrate the ability of our new algorithm to better maintain the shape of the
solution in the presence of shocks and discontinuities.