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Math Help - Backward Euler Method for 2x2 systems

  1. #1
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    Backward Euler Method for 2x2 systems

    Hi!!!
    I want to write a code in Matlab for the Backward Euler Method for 2x2 systems, using the fixed point iteration to find the yn+1.
    y1n+1=y1n+h*f(tn+1,y1n+1,y2n+1) (1)
    y2n+1=y2n+h*g(tn+1,y1n+1,y2n+1) (2)
    Could you tell how I use the fixed point iteration??
    At (1) the fixed point iteration will calculate y1n+1, y2n+1 will be calculated at (2) but it is already used in the equation (1) ...
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  2. #2
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    Re: Backward Euler Method for 2x2 systems

    The fixed point algorithm should be the same as the one for single equation but the iteration function function will be a 2*1.


    w1=y1+h*f(t,y1,y2)
    w2=y2+h*g(t,y1,y2)
    w=[w1;w2]
    the iteration equation then
    while y-y_1<tol
    y=w
    end
    the solutions are:
    y1=y(1)
    y2=y(2)

    hope that helps!
    Thanks from mathmari and topsquark
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  3. #3
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    Re: Backward Euler Method for 2x2 systems

    Ok! Thank you!!!
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