Ode45: Theory and how the interpolation works [Matlab] скачать в хорошем качестве

Ode45: Theory and how the interpolation works [Matlab]

In this video, we're going to take a look at how the ode45 works. We'll start by taking a look at numerical integrators in general. Then, we'll dive into what a Butcher-Tabelau is and how they can be used. Afterwards, we'll dive into the specifics of the ode45, how it's implemented in MATALB, and how the interpolation is realized. Addition to 10:00: For the first 200 values, the preallocated memory is used and the simulation time, state and k-values are saved with the lines 382, 383 and 384 in the code. Only afterwards (if more steps are required) are the three lines used, that I marked in the code. Visual bug around 8:10: I have no clue, how to get rid of those strange visual bugs visible around 8:10... they are not always there in edditing mode, but when I export the video they show up. Other video in the series covering dynamic simulation and background: Introduction into dynamic Simulation (overview, also covering numerical integrators briefly):    • Introduction into dynamic Simulation (Over...   Simulation of accelerating Vehicle (introduction into dynamic simulation):    • Simple vehicle simulation [Matlab, Dynamic...   Simulation of baseball influenced by air resistance (nonlinear model, event handling):    • Simulation of baseball trajectory with air...   Simulation of a box sliding down a wedge (last Video in the Series):    • Simulation: Box on Wedge [Matlab, Dynamic ...   Example, where ode45 can cause issues (next Video in the Series):    • Ode45: When it causes issues and how to fi...   Tags/ Keywords: Dynamic Simulation, Numerical integrators, ode45, Interplation ode45 Sources metioned: Dormand, J. R. and P. J. Prince, “A family of embedded Runge-Kutta formulae,” J. Comp. Appl. Math., Vol. 6, 1980, pp. 19–26. Shampine, L. F. and M. W. Reichelt, “The MATLAB ODE Suite,” SIAM Journal on Scientific Computing, Vol. 18, 1997, pp. 1–22. Chapters: 00:00 - Introduction 01:08 - Numerical Integration 05:27 - Ode45 (Math) 08:40 - Ode45 (MATLAB) 10:35 - Interpolation 13:35 - Outlook