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# Euler's Method

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I have to use Euler's method on a problem..I don't really know what I'm doing...

This is exactly what my book says is the sequence for Euler's Method:

y(xi+1) ≈ yi +1 = yi + hf(x, yi),     for i = 0, 1, 2, . . .

My quesion is what is f(x, yi) ???

What is there a comma doing in there???

Here is the actual question that I have to answer:

Use Euler's methos with h = 0.1 to approximate y(1). Show the first 2 steps by hand.

y' = 2xy, y(0) = 1

Mar 29, 2017

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Let me  see if I remember this, hectictar.....

y' = f (x, y)  = 2xy

The initial condition says that y(x0) = y0   ...so..... y(0)  = 1 and  (x0, y0)   = (0, 1)

So   f( x0, y0  )  = 2(x0)(y0)  =   2(0)(1)  =  0

And  h = .1     [ this is known as the step size ]

So....we   need to find   (x1, y1)

x1   =   x0  +  h  =    0 + .1   =  .1

y1 = y0 + h f(x0, y0)  =    1 +  .1 ( 0)  =  1

So......our second point (x1, y1)  is  (.1, 1)        and  f (x1, y1)  =  2(.1)(1)  =  .2

Now.......find  (x2, y2 )

x2   =   x1  +  h  =    .1 + .1   =  .2

y2 = y1 + h f(x1, y1)  =    1 +  .1 ( .2)  =  1.02

So.....our third point (x2, y2) is  (.2, 1.02)  and   f (x2, y2 )  =  2(.2)(1.02)   = .408

This iteration continues until  we get to  x10    = 1

I assume you have some program that you can use to do this???...it's very time consuming, by hand!!

Anyway ......  Here's a pretty good explanation of the method :

http://calculuslab.deltacollege.edu/ODE/7-C-1/7-C-1-h-c.html   Mar 29, 2017
#2
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Thank you very much CPhill! This helped a lot!  ( Those are the same answers as the book for y1 and y2 )

I actually don't have a program that can do it...my friend said that there was a website that can do this, so I will try to find that. If not I might can come up with something that will work in excel....

Mar 30, 2017
#4
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I wanna say that you're looking ugly hhahaha

Apr 5, 2017