{"version":"1.0","type":"rich","title":"just took the derivative of rk4 by hand...","description":"This example shows the step-by-step derivation of the Jacobian matrix update for the Runge-Kutta 4 (RK4) method, displayed as MATLAB code. It first presents the full, unwieldy one-line expression for the derivative, then reorganizes it into a clearer, more readable sequence of intermediate variables. The code computes the local error propagation by multiplying Jacobian evaluations (via `feval` with a function handle `J`) at successive RK4 stages, accumulating products with identity matrices scaled by step size `h`. The final result updates the matrix `L` using the weighted sum of these Jacobian products, demonstrating how to propagate sensitivities through the RK4 integrator.","provider_name":"VizHub AI Studio","provider_url":"https://next.vizhub.com","html":"<iframe src=\"https://next.vizhub.com/viz/gist-7905737?mode=embed\" width=\"960\" height=\"500\" scrolling=\"no\" frameborder=\"1\"></iframe>","width":960,"height":500,"cache_age":3600}