A variable nonlinear splitting algorithm for reaction diffusion systems with self‐ and cross‐ diffusion

Self‐ and cross‐diffusion are important nonlinear spatial derivative terms that are included into biological models of predator–prey interactions. Self‐diffusion models overcrowding effects, while cross‐diffusion incorporates the response of one species in light of the concentration of another. In this paper, a novel nonlinear operator splitting method is presented that directly incorporates both self‐ and cross‐diffusion into a computational efficient design. The numerical analysis guarantees the accuracy and demonstrates appropriate criteria for stability. Numerical experiments display its efficiency and accuracy.