Stability and errors estimates of a second-order imsp scheme

We analyze a second-order accurate implicit-symplectic (IMSP) scheme for reaction-diffusion systems modeling spatiotemporal dynamics of predator-prey populations. We prove stability and errors estimates of the semidiscrete-in-time approximations, under positivity assumptions. The numerical simulations confirm the theoretically derived rates of convergence and show an improved accuracy in the second-order IMSP in comparison with the first-order IMSP, at same computational cost.