Lipschitz conditions are connected with contractive. As an example, three functions satisfying this condition with dierent values of Îº are displayed on figure. Theorem 15 fast rates let f lipk be any lipschitz function satisfying condition 1 for some Îº 1, cÎº. The constant l is called a lipschitz constant for.
This function is continuously dierentiable. The condition has an obvious generalization to vector. Pick up any point x r, we observe that. The term is used for a bound on the modulus of continuity a function. Satisfies the lipschitz condition on.
This is a basic introduction to lipschitz conditions within the context of differential equations. We will show that f1 is locally lipschitz-continuous but not globally so. We will examine them in turn, with b 1. The functions below are pictured in gure.
We now turn our attention to the general initial value problem.