Positivity and boundedness preserving schemes for spacetime fractional predatorprey reactiondiffusion model
The semi-implicit schemes for the nonlinear predatorprey reactiondiffusion model with the spacetime fractional derivatives are discussed, where the space fractional derivative is discretized by the fractional centered difference and WSGD scheme. The stability and convergence of the semi-implicit schemes are analyzed in the L? L ? norm. We theoretically prove that the numerical schemes are stable and convergent without the restriction on the ratio of space and time stepsizes and numerically further confirm that the schemes have first order convergence in time and second order convergence in space. Then we discuss the positivity and boundedness properties of the analytical solutions of the discussed model, and show that the numerical solutions preserve the positivity and boundedness. The presented numerical examples confirm the theoretical results and convergence orders.
semi-implicit scheme fractional centered difference wsgd scheme spacetime fractional model