A Second-Order Accurate, Operator Splitting Scheme for Reaction-Diffusion Systems in an Energetic Variational Formulation

A second-order accurate in time, positivity-preserving, and unconditionally energy stable operator splitting scheme is proposed analyzed for reaction-diffusion systems with the detailed balance condition. The designed based on an energetic variational formulation, which reaction part reformulated terms of trajectory, both diffusion parts dissipate same free energy. At stage, trajectory equation approximated by a Crank--Nicolson type method. unique solvability, positivity-preserving property, stability are established convexity analysis. In exact integrator applied if coefficients constant, constructed nonlinear. either case, property could be theoretically established. Moreover, combination numerical algorithms at stages Strang approach leads to accurate, structure-preserving original system. Numerical experiments presented, demonstrate accuracy scheme.