Figure 4.

Step size restrictions of the numerical methods Largest ratio Δt/τ for which the different numerical methods (blue curve: Euler-Maruyama method, black curve: implicit Euler method solved with fixed-point iteration, red curve: scalar exponential Euler method) are stable shown against the absolute value of λ_max = argmax_λi ζ (λ_i) ∈ ℝ. The gray area indicates the region where the scalar exponential Euler method and the implicit Euler method are stable without any restrictions on Δt/τ. The dotted vertical lines correspond to the examples presented in the panels of Figure 2.