Approximating k with Shooting Method and Euler's Method

[androol]

dy/dt = ky, where k is a constant.
y|t=0 = 1; y|t=10 = 4

I need to approximate k using the shooting method and Euler's method... please help.. :)

wat's the procedure to approximate k using the shooting method

 

[HallsofIvy]

Do you know what "Euler's method" is?

Start with an easy estimate: take dt= 5 so we have only two steps
Initially, t= 0, y= 1, so dy/dt= k and dy= 5k

then t= 5, y= 1+ dy= 1+ 5k so dy/dt= k(1+ 5k)= k+ 5k² and so dy= 5(k+ 5k²)= 5k+ 25k².

Finally, then, x= 10, y= 1+ 5k+ dy= 1+ 5k+ 5k+ 25k²= 1+ 10k+ 26k²= That is, 25k²+ 10k- 3= 0. Solve that for k.

Now that you know, roughly, k, use, say, 10 steps from x= 0 to x= 10 with that k and see if you get 4 there. You won't of course, but that will tell you whether to make k smaller or larger. Do that repeatedly until you get a good method.