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Use Euler's method with h=0.1 to find approximate values?

  1. Dec 5, 2014 #1
    1. The problem statement, all variables and given/known data
    Use Euler's method with h=0.1 to find approximate values of the solution of the initial-value problem y'+3y=7e^(4x), y(0)=2 at x=0, 0.1, 0.2, 0.3, ..., 1.0.

    2. Relevant equations
    f(x, y)=7e^(4x)-3y
    x0=0, y0=2

    3. The attempt at a solution
    y(0.1)=y1=y0+f(0, 2)(0.1)=2+(0,1)f(0, 2)=2.1
    y(0.2)=y2=y1+f(0.1, 2.1)(0.1)=2.1+(0.1)f(0.1, 2.1)=2.51428
    And so on...
    But am I doing it right? If not, then please correct me.
     
  2. jcsd
  3. Dec 5, 2014 #2
    Looks good so far.

    You could use a table format like this to show the rest of your results:

    $$
    \begin{array}{|c|c|c|c|c|c|c|}
    \hline
    \text{Step }n & y_n & x_n & f(x_n,y_n) & h & \Delta y & y_{n+1} \\
    \hline
    0 & 2 & 0 & 1 & 0.1 & 0.1 & 2.1 \\
    \hline
    1 & 2.1 & 0.1 & 4.1428 & 0.1 & 0.41428 & 2.51428 \\
    \hline
    2 & 2.51428 & 0.2 & ?? & 0.1 & ?????? & ??????? \\
    \hline
    3 & ??????? & 0.3 & ?? & 0.1 & ?????? & ??????? \\
    \hline
    4 & ??????? & 0.4 & ?? & 0.1 & ?????? & ??????? \\
    \hline
    5 & ??????? & 0.5 & ?? & 0.1 & ?????? & ??????? \\
    \hline
    6 & ??????? & 0.6 & ?? & 0.1 & ?????? & ??????? \\
    \hline
    7 & ??????? & 0.7 & ?? & 0.1 & ?????? & ??????? \\
    \hline
    8 & ??????? & 0.8 & ?? & 0.1 & ?????? & ??????? \\
    \hline
    9 & ??????? & 0.9 & ?? & 0.1 & ?????? & ??????? \\
    \hline
    \end{array}
    $$
     
  4. Dec 5, 2014 #3
    Do I nee to solve for y(1)? Because it says x=0, 0.1, 0.2, 0.3, ..., 1.0.
     
  5. Dec 5, 2014 #4

    Mark44

    Staff: Mentor

    Yes. I don't know why you would think you don't need to.

    y(1) means the y value when x = 1.0.
     
  6. Dec 5, 2014 #5

    Mark44

    Staff: Mentor

    PF now supports various table bbcode tags, an alternative to using LaTeX. Here are the header row and two rows of the first three columns of the table above.
    [TABLE]
    [TR][TH]Step (n)[/TH][TH]yn[/TH] [TH]xn[/TH][/TR]
    [TR][TD1]0[/TD1][TD1]2[/TD1] [TD1]0[/TD1] [/TR]
    [TR][TD1]1[/TD1][TD1]2.1[/TD1] [TD1]0.1[/TD1] [/TR]
    [/TABLE]
     
  7. Dec 5, 2014 #6
    So the answer starts with y1 to y10, right?
     
  8. Dec 5, 2014 #7
    Those are the numbers requested. Note that in the table I gave you, y10 is in the bottom right corner - this is our Euler-method estimate of y(1.0)


    Thanks... not sure which I prefer really, but the compact output is good.
     
    Last edited: Dec 5, 2014
  9. Dec 5, 2014 #8

    Mark44

    Staff: Mentor

    I don't which I like better either. It's pretty much six of one, half a dozen of the other.
     
  10. Dec 6, 2014 #9
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