Figure 2.

Accuracy of numerical methods for two networks of linear rate units. $RMSE=\sqrt{\frac{1}{N(t_n-t_0)}\sum _{i=1}^N\sum _{j=1}^n{(X_j^i-{\hat{X}}_j^i)}^2}$ of the solution X obtained by the approximate solvers (blue curve: Euler-Maruyama method, black curve: implicit Euler method solved with fixed-point iteration, red curve: scalar exponential Euler method) with respect to the reference solution $\widehat{X}$ as a function of step size in double logarithmic representation. The respectively colored vertical lines mark the largest tested step size for which the corresponding methods deliver a solution with RMSE ≤ 10¹⁰. RMSE computed over 200.0 ms of biological time. (A) Inhibitory all-to-all test case. Network parameters: N = 400, μ = 0, σ = 10 and τ = 1 ms. (B) Sparse balanced e/i test case. Network parameters: N = 400, p = 0.2, μ = 0, σ = 10 and τ = 0.5 ms.