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Math Help - Picard Iteration

  1. #1
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    Picard Iteration

    I'm doing some revision and I'm having some trouble understanding the principle behind picard's iteration.I tried to do some practice by tackling the following problem but I got nowhere as I don't know with what should I substitute f(s,u(s)) in the integral.
    The problem states the following:
    u'= v and v'= −u
    with initial conditions u(0) = 1 and v(0) = 0, find an approximate solution by
    performing 4 steps of Picard iteration and compare the results with the actual solution.
    If someone has the time and patience to enlighten me with a step by step explanation that will be incredible.
    Thanks at least for taking the time to read this
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  2. #2
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    Quote Originally Posted by PatrickM View Post
    I'm doing some revision and I'm having some trouble understanding the principle behind picard's iteration.I tried to do some practice by tackling the following problem but I got nowhere as I don't know with what should I substitute f(s,u(s)) in the integral.
    The problem states the following:
    u'= v and v'= −u
    with initial conditions u(0) = 1 and v(0) = 0, find an approximate solution by
    performing 4 steps of Picard iteration and compare the results with the actual solution.
    If someone has the time and patience to enlighten me with a step by step explanation that will be incredible.
    Thanks at least for taking the time to read this
    Dear PatrickM,

    I don't think this problem could be done using Picard iteration method. The Picard iteration method may be applied for a first order differential equation with a given boundary condition. However in this case there are two first order differential equations with unknowns v and u. So you could solve this system by representing the two equations in matrix form.
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