estimate_rms_residuals(fun, sol, x, h, p, r_middle, f_middle)
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 , 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.
Estimated rms values of the relative residuals over each interval.
Estimate rms values of collocation residuals using Lobatto quadrature.
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them