Question

Use a technological tool and Euler's method with ten steps of size 0.1 to estimate y(1) for differential equation dy/dx=y-2. Make certain to include supporting screen captures.

Answer 1

write a small sweet program..
euler's method is just a linear method in short steps, you keep updating your "y" and timestep.
fortran, C and python are the programming choices. if you have access, you may want to try matlab or octave

Answer 2

i dont know whats matlab or octave...i do have internet

Answer 3

you know, its easy. you can implement it on excel as columns!!!! as you drag it down the next row should get updated!

Answer 4

no we need to do it by ourself

Answer 5

yea.. ok. open up the excel.

Answer 6

and how to use euler's method here

Answer 7

done have one dude

Answer 8

you mean by "hand"?> it says use technological tool.

Answer 9

you do not have Microsoft Excel?

Answer 10

nop

Answer 11

ya i meant euler's method by hand and technological tool by internet

Answer 12

ok.
step 1) initial things
iteration n
\(h=0.1\) = time step.
\(f(x,y) =y-1\) -> equation for update

Answer 13

what are the initial conditions?

Answer 14

i really dont know

Answer 15

that must be provided
y(0)=?

Answer 16

1

Answer 17

it is 1

Answer 18

that is the initial condition when \(x_0=0\)

Answer 19

i know y(0) = 1...where did you get x0 = 0 from

Answer 20

oh ya it is given nm

Answer 21

we have \(x0=0,\;y0=1\)

iter# 0
\(y_1=y_0+hf(x_0,y_0)=1+(0.1)(1−2)=0.9\)
\(x_1=x_0+h=0+0.1=0.1\)

Answer 22

iter# 1
\(y_2=y_1+hf(x_1,y_1)=0.9+0.1(0.9−2)=0.79\)
\(x_2=x_1+h=0.1+0.1=0.2\)

Answer 23

iter# 2
\(y_3=y_2+hf(x_2,y_2)=0.79+0.1(0.79−2)=0.669\)
\(x_3=x_2+h=0.2+0.1=0.3\)

Answer 24

and you keep going till you get to iter# \(n=10\)

Answer 25

it is so long lol...isnt there any shortcut

Answer 26

like I said, some programming tool.

Answer 27

ok lemme go until n=10...thrn call you back...we will discuss on technological tool then

Answer 28

whats iter

Answer 29

iter = short for iteration..

btw, your answer should be close to (not exact) analytical solution
\(y(1)=2-e\)

Answer 30

ohk