 Picard iterate

A Picard iterate is one of the successive approximate solutions of a differential equation obtained by repeatedly applying its integral solution operator. If $y^{\prime }=f(t,y)$ 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.