Shooting Method for Boundary Value Problems | Lecture 57 | Numerical Methods for Engineers

How to solve a two-point boundary value problem differential equation by the shooting method.

[Caspar__]

The way he is writing this xi, I feel this.

[mathoph]

Very useful sketch at the end, it is clear enough why it is called "shooting"

[Rossenboy]

Really well explained with the figure. Thank you!

[eh]

Thank you very much for all the clear explanation! It is really helpful.

[eniemeuful]

4:35 I still don't get the definition of F.

[statitik]

The question may sound weird, but how exactly is F(xi) = y(x_f) - y_f dependent on xi?
Does it mean that my xi dictates how I start from y(0) (i.e. z(0) = xi = slope) and how the function "evolves over time" given z(0) = xi, such that if xi was chosen right I get F(xi) = 0 (i.e. I hit the right target for y(x_f))? In other words: F(xi) denotes how the function y evolved for a particular xi. Am I right?

And God alone knows best.

[marcinknapik]

Is this video horizontally flipped or is the author able to write in reverse?

[pedrocalorio]

Just to comment on this last sentence, you use fzero or fsolve for the root-finding and ode45 for the integration, couldn't you use an optimizer for satisfying both?

[pedrocalorio]

Hey Jeffrey,

That is a pretty good explanation of the boundary value problem, thanks a lot for that.

Now I have a question about something that doesn't seem to get to my head, at least for now.

Let's say we have a boundary value problem and we turn this into an NLP such the dynamics of our system become the constraints, and we are trying to minimize a function that depends on the states and in the set of control inputs of this hypothetical system. When we call, for example, fmincon to solve this, this solver internally is solving these differential equations each iteration and evaluating the function F(j) = y(xf)-yf and persuing to minimize it, so in the end, you have all your states and control inputs that make this function goes to zero and thus have your final time constraints met?

[muhammadarif]

Hi jaffery plz give refrence for more study

[LL-wuui]

I'm stuggling when I have given Neumann boundary condition and I need to find y(x_0)=y_0.

:(

[PixiiGER]

I really like the fact, that we can see you while writing, but my brain starts itching seeing you write from left to right. I guess the video is simply mirrored, but still :D
Good lesson anyway :P