Calling Euler Method to solve Shooting Method

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Hi, I am trying to solve a BVP:
y''(x) +5y'(x)+4y(x) = 1 with boundary conditions y(0) = 0 and y(1)=1
using shooting method.
I found many examples by solving such BVP using ode45 but I want to solve it by euler method (not allowed to use built-in command), but I got stuck in doing so.
I need help to do so...

Accepted Answer

Alan Stevens
Alan Stevens on 9 May 2021
You need to express your 2nd order ode as two 1st order odes
y``(x) + 5y`(x) + 4y(x) = 1
v = dy/dx
dv/dx = y``(x)
So you have
y`(x) = v(x)
v`(x) = 1 - 4*y(x) - 5*v(x)
Now your Euer expressions become
t(i) = t(i-1) + h;
y(i) = y(i-1) + h*v(i-1);
v(i) = v(i-1) + h*(1 - 4*y(i-1) - 5*v(i-1));
and you must supply initial values for both y and v.

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