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Differential Equations Euler's method

  1. Feb 19, 2013 #1
    Find the solution y = φ(t) of the given problem and evaluate φ(t) at t = 0.1, 0.2, 0.3,
    and 0.4.

    1.y'=3+t-y
    y = φ(t)=t-2e^-t
    y(1)= 0+(0-2e^0)*(.1)=.8
    and the correct answer is 1.19516

    2. y'=2y-1

    What I'm getting stuck on is do I use the formula y(n)=y(n-1)+f(t(n-1),y(n-1)h because when I do I do not get the same answers as back of the book.

    Thanks for the help!
     
  2. jcsd
  3. Feb 20, 2013 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Where did you get this? With y= t- 2e^{-t}, y'= 1+ 2e^{-t} while 3+ t- y= 3+ t+ t- 2e^{-t}= 3+ 2t- 2e^{-t}. They are NOT the same. In any case, you cannot get a specific solution to this without some "initial condition".

    You are using Euler's method for this? Yes, Euler's method approximates y'= dy/dx by [itex]\Delta y/\Delta x= \Delta y/h[/itex] so your equation becomes [itex]\Delta y/h= f(t, y)[/itex] so that [itex]\Delta y= y_n- y_{n-1}= f(t, y)h[/itex] so that [itex]y_n= y_{n-1}+ f(t, y)h[/itex]. For this problem, f(t, y)= 2y- 1 so you just have [itex]y_n= y_{n-1}+ (2y_{n-1}-1)h[/itex]. What did you get?
    (And, again, you cannot solve a first order differential equation for a specific value with an "initial condition". What are you using for t0 and y0?

     
    Last edited: Feb 20, 2013
  4. Feb 20, 2013 #3
    y(0)=1/2
     
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