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Math Help - Numerical Approximatin: Euler's Method

  1. #1
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    Numerical Approximatin: Euler's Method

    These problem are also due in two days. I just wanted to post them separately because they're two different subjects.Thanks.

    1) Apply Euler's Method with h=0.1 to approximate the solution of the initial value problem ==> y'= y- x- 1, y(o)=1 <=== on the interval [0, 1/2]

    2) Apply Euler's Method with h=0.25 to approximate the solution of the initial value problem ==> y'=y- x- 1, y(0)=1 <=== on the interval [0, 1/2]

    3) Given the initial value problem: dy/dx= y, y(0)= 1. Do the following:

    a. Solve the initial value problem and show that e= y(1).
    b. Apply Euler's Method with h= 0.25 to approximate e= y(1).
    c. Apply improved Euler's Method with h=0.5 to approximate e=y(1).
    d. Apply Runge-Kutta Method with h=1 to approximate e= y(1).
    e. Find errors of the above approximations of e. Wich approximation is the best?
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  2. #2
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    Quote Originally Posted by googoogaga View Post
    These problem are also due in two days. I just wanted to post them separately because they're two different subjects.Thanks.

    1) Apply Euler's Method with h=0.1 to approximate the solution of the initial value problem ==> y'= y- x- 1, y(o)=1 <=== on the interval [0, 1/2]
    see attachment.

    RonL
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  3. #3
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    I have no clue of what that means.

    Could you please explain in lamer terms?
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  4. #4
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    Quote Originally Posted by googoogaga View Post
    Could you please explain in lamer terms?
    First col contains x_0, x_1, .., third col is y'(x_n), first element of second
    col is y(x_0), subsequent terms are y(x_{n-1})+hy'(x_{n-1}), h=delta\_x

    RonL
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