Picard-Lindelöf theorem Guide, Meaning , Facts, Information and Description
In mathematics, the Picard-Lindelöf theorem on existence and uniqueness of solutions of differential equations (Picard 1890, Lindelöf 1894) states that an initial value problem
has exactly one solution if f is Lipschitz continuous and bounded.
A simple proof is successive approximation: (also called Picard iteration)
Set
and
It can then be shown rather easily that the sequence of the (called the Picard iterates) is convergent and that the limit is a solution to the problem.
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