Everything you need to know about Initial Value Problem Solvers
نویسنده
چکیده
2.1 Definition: Lipschitz Function A real valued function f : D ⊆ R → R is called Lipschitz continuous or is said to satisfy a Lipschitz condition if there exists a constant K ≥ 0 such that for all x1, x2 in D |f(x1)− f(x2)| ≤ K|x1 − x2| (3) The inequality is (trivially) satisfied if x1 = x2. Otherwise, for x1 6= x2, one can equivalently define a function to be Lipschitz if and only if |f(x1)−f(x2)| |x1−x2| ≤ K that is, iff the slopes of all secant lines are bounded.
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