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Math Help - [SOLVED] Numerical solutions of ordinary dif eqs

  1. #1
    olionel
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    [SOLVED] Numerical solutions of ordinary dif eqs

    Hello there;

    I have a wee question, itd be great if I can get a solution for this. (I am putting it up on behalf of a friend as Im not really sure where to start, hes studying maths at uni.... Im a lazy engineer that asks mathemticians )

    Thanks!

    The question is

    solve (1+x^2)y'' - xy'- 3y = 6x-3 with

    y(0)-y'(0)=1

    y(1)=2 on [0,1]

    with h=0.2

    hint: use central difference for each derivatives.
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by olionel View Post
    Hello there;

    I have a wee question, itd be great if I can get a solution for this. (I am putting it up on behalf of a friend as Im not really sure where to start, hes studying maths at uni.... Im a lazy engineer that asks mathemticians )

    Thanks!

    The question is

    solve (1+x^2)y'' - xy'- 3y = 6x-3 with

    y(0)-y'(0)=1

    y(1)=2 on [0,1]

    with h=0.2

    hint: use central difference for each derivatives.
    Tell your friend to start by substituting the difference quotients

    y_i^{''} = \frac{y_{i+1} - 2y_i + y_{i-1}}{h^2}

    and

    y_i^{'} = \frac{y_{i+1} - y_{i-1}}{2h}

    into the ODE. Simplify the result to get a difference equation of the form ay_{i+1} + by_i + cy_{i-1} = d.

    There are five (why?) unknowns: y_0, y_1, y_2, y_3, y_4. y_5 = 2 (why?)

    Use the difference equation to obtain four equations involving these unknowns. And don't forget that y_0 - y^{'}_0 = 1 (why?). Set up the matrix equation representing these equations. Solve for the unknowns.
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  3. #3
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    Joined
    Jan 2008
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    hi,

    i am the friend of olionel call me lazy mathematician :P

    mr fantastic, thanks for your reply i got the result

    now i need to write it in Mathematica and plot the graphiscs ( approximate solution and exact solution ) anyhelp about Mathematica would be great
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