= Picard iterate
{c}
{title2=$y_{n+1}=Ty_n$}
A <Picard iterate> is one of the successive approximate <solutions of a differential equation> obtained by repeatedly applying its integral solution operator. If $y'=f(t,y)$ and $y(0)=b$, the usual operator is $(Ty)(t)=b+\int_0^t f(s,y(s))\,ds$. An <integrating factor> can produce a different, equivalent operator with better estimates, as in <Global Picard iteration with a decaying kernel>. The word iterate denotes an approximate function; <Picard iteration> denotes the procedure.
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