scipy.integrate._bvp:estimate_rms_residuals

Extended Summary

The residuals are defined as the difference between the derivatives of our solution and rhs of the ODE system. We use relative residuals, i.e., normalized by 1 + np.abs(f). RMS values are computed as sqrt from the normalized integrals of the squared relative residuals over each interval. Integrals are estimated using 5-point Lobatto quadrature ^[1], we use the fact that residuals at the mesh nodes are identically zero.

In [2] they don't normalize integrals by interval lengths, which gives a higher rate of convergence of the residuals by the factor of h**0.5. I chose to do such normalization for an ease of interpretation of return values as RMS estimates.