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Euler's Method

  1. Jun 8, 2012 #1
    1. The problem statement, all variables and given/known data

    I have some trouble understanding the following solved problem:

    http://img808.imageshack.us/img808/3340/euler2.jpg [Broken]

    This is the solutions they have given us:

    [itex]E(32 \ steps) = 0.00097030[/itex]

    [itex]E(64 \ steps) = 0.00003202[/itex]

    32 steps has h=0.625

    64 steps has h= 0.03125

    The formula for effective order at stepsize h is

    [itex]q= \frac{\ln |E(2h)|- \ln |E(h)|}{\ln 2}[/itex]

    [itex]\therefore q (0.03125)= \frac{\ln |E(0.625)|- \ln |E(0.03125)|}{\ln 2} \approx 4.92[/itex]

    3. The attempt at a solution

    So I don't understand how they figured out that 32 steps has a step size of 0.625? What is the relationship between the stepsize and number of steps? :confused:

    I used to think that step size and the number of steps were related like this:

    [itex]h = \frac{1}{step \ size}[/itex]

    But using this, for 32 steps I get a step size of h=1/32=0.03125, and for 64 steps I get h=1/64=0.0156. The only way I can get the correct answer is to multiply the denominator by 2, but why should I do that?

    So, what's the problem with what I'm doing? Is my method wrong, or is that a typo in the given answers?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jun 8, 2012 #2
    The problem states that y(1) = -1, and the solutions are at t=3.
    The step size would be the change in t divided by the number of steps.
     
  4. Jun 9, 2012 #3
    But still I don't get the correct answer. The correct answer says:

    And if I divide the change in t by the number of steps I get

    2/32=0.0625

    2/64=0.03125

    How come for 32 steps I got a different answer?
     
  5. Jun 9, 2012 #4
    I'm not sure. It's weird that the number they gave is off by a factor of 10, but the one for 64 is correct. Is it possible it's a typo?
     
  6. Jun 9, 2012 #5
    Yes. But are you sure in order to find the step size from the number of steps we have to divide the change in t by the number of steps? If that's the correct method then I think that may be a typo.
     
  7. Jun 9, 2012 #6

    vela

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    Yes, Villyer is correct, and that's a typo.
     
  8. Jun 9, 2012 #7
    Okay thank you very much for the confirmation. And thanks a lot Villyer!!
     
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