On estimation of the global error of numerical solution on canard-cycles

Under study is the behavior of the global error of numerical integration in the two-variable mathematical model of a heterogeneous catalytic reaction. Numerical estimation of the global error indicates that there is a high sensitive dependence of the solutions on initial conditions due to the existence of a tunnel-type bundle of trajectories which is formed by the stable and unstable canards. We show that the exponential growth of the norm of the fundamental matrix of solutions of the system linearized around a stable canard-cycle yields exponential growth of the leading term in the global error of numerical solution.