Calling Euler Method to solve Shooting Method

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...

Thanks,

Answer 1

[Alan Stevens]

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.

[Muhammad Usman]

Thanks

[Hira Nur Yesiloglu]

mr.usman do you have the complete code using euler?

[Fareeha]

how will we use built in command to solve this problem?

[Torsten]

@Fareeha

Use "bvp4c" or - for simple problems as the one given - "dsolve".

If you are forced to use the shooting method, combine "ode45" and "fsolve".

syms y(x) 
ysol = dsolve(diff(y,2)+5*diff(y,x)+4*y(x)==1,[y(0)==0,y(1)==1])