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Homework Help: Numerical analysis

  1. Mar 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Consider the equation
    y0 = Ly; y(0) = 1:
    **L = lamda**
    Verify that the solution to this equation is y(t) = e^(Lt). We want to solve this equation numerically to obtain an approximation to y(1). Consider the two following methods to approximate
    the solution to this equation:
    Method I: y_(n+1) = y_(n) + hf(y_(n+1); t_(n+1))
    Method II:y_(n+1) = y_(n) +(h/2)*(f(y_(n); t_(n)) + f(y_(n+1); t_(n+1)))

    (a) Compute the truncation error for both methods. Which one is more accurate?
    (b) i was able to do this one!!
    (c) Obtain an expression for y_(n+1) as a function of y0 for methods I and II.
    (d) Using the expressions obtained in the previous part, compute lim (as n goes to inf) y_(n)
    (Remember: h = 1/n).
    (e) In view of the results in the previous part, do the methods converge?
    (f) Assume that h = :1, and L = -1000. Plot y0, y1, y2, y3, and y4 for both
    methods. Plot the function y(t) = e^(Lt). In view of these plots, which method performs

    i am just soo lost when it comes to solving this problem. i have idea how to approach it. any help with this will be greatly appreciated!
  2. jcsd
  3. Mar 16, 2009 #2


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    Science Advisor

    Surely this isn't what you meant. Did you mean y'= Ly?

  4. Mar 16, 2009 #3
    yes that is what i meant, sorry, working on this for a long time... kinda burnt out
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