1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    better?

    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

    HallsofIvy

    User Avatar
    Staff Emeritus
    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Numerical analysis
  1. Numerical Analysis (Replies: 2)

  2. Numerical analysis (Replies: 5)

  3. Numerical analysis (Replies: 1)

  4. Numerical Analysis (Replies: 3)

Loading...