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...
Thanks,
采纳的回答
Alan Stevens
2021-5-9
0 个投票
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.
4 个评论
Muhammad Usman
2021-5-11
Hira Nur Yesiloglu
2022-6-7
mr.usman do you have the complete code using euler?
Fareeha
2024-11-24
how will we use built in command to solve this problem?
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])
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