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Calculate Picard Iterates for the IVP ![diff(y(x), x) = f(x, y(x)), y(x[0]) = y(x)[0]](/support/helpjp/helpview.aspx?si=4033/file05459/math7.png)
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Description
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Calculate an iterative solution to an ODE by using Picard's method.
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Picard Iterates for the IVP ![diff(y(x), x) = f(x, y(x)), y(x[0]) = y(x)[0]](/support/helpjp/helpview.aspx?si=4033/file05459/math37.png)
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The function 
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| (1) |
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Set ![a = x[0]](/support/helpjp/helpview.aspx?si=4033/file05459/math57.png)
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| (2) |
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Set ![phi[0] = y(x[0]) and y(x[0]) = y[0]](/support/helpjp/helpview.aspx?si=4033/file05459/math71.png)
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![phi[0] := 0](/support/helpjp/helpview.aspx?si=4033/file05459/math76.png)
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| (3) |
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Number of iterates
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| (4) |
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Picard Iterates
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![for k from 0 to N-1 do phi[k+1] := unapply(phi[0]+int(f(t, phi[k](t)), t = __a__ .. x), x); print(nprintf("Iterate number %d:", k+1))*print(phi[k+1](x)) end do:](/support/helpjp/helpview.aspx?si=4033/file05459/math100.png)
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| (5) |
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