“Picard's theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Picard's theorem

释义

Picard's theorem

An iterative method for solving the initial-value problem:

Assume that f is a continuous function in the first variable and Lipschitz in the second variable. Then there exists an open interval about x0 on which there is a unique solution y(x). The solution can be constructively found as the limit of functions yn(x), where

As an example, suppose dy/dx = y and y(0) = 1. Then

So yn(x) is the first n + 1 terms of the exponential series and converges to the solution y(x) = ex.

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