Shooting method for BVP

Hi Guys,

This is a tough module and the textbook is very complicated.

Is there someone out there that could maybe help me to understand how they got to the results of example 6.2 (p. 369 G&W 7th ed.).

I also saw that this text is full of typos, hence i do not know if the question contains a typo or what.

Thanx.

firstly i'd like to say that the numerical methods textbook is easily the best thing about going to unisa for me! it's excellent, typos aside.

i haven't properly looked at the shooting method, but from the name and briefly reading the description, it sounds like you pick an arbitrary-ish starting value, follow the differential equation to the x-value where your boundary condition is defined. most likely you won't hit the exact y-value for which the boundary condition is given, so the whole process becomes a search problem: which initial value gets me (by following the DE) to the right value where the boundary condition is defined?

this kind of makes sense to me, but again i haven't properly looked at it yet (suffering mat307 atmo, just squizzed the abstract description of the method) so what i wrote could well be wrong. have a look online (eg. wikipedia), i'll look there eventually too...

edit: typing this out actually cleared it up for me a bit, so i looked around online (too lazy to get my book out the cupboard, lol) and it seems my guess wasn't too far off . some resources:

http://en.wikipedia.org/wiki/Shooting_method
http://numericalmethods.eng.usf.edu/topics/shooting_method.html

Hi,

I am with you on this one. I am no math genius and feel the Book assumes too much and explains too little.

Pg 359 - Explains how they have split f=m*d²x/dt² into dx/dt = y and dy/dt = f/m.

Pg 360 - Eg. 6.2 - then uses two arbitrary equations to try and explain how to use them for Taylor-Series, Euler Predictor....I understand this much and this seems simple enough.But know I have tried applying it to Q1 in Assignment 3 and then I am struggling.

On Pg 361 - the equations for x_p , y_p , x_c and y_c are only examples. What are the actual equations?