A numerical approach to the proof of existence of solutions for elliptic problems II
A numerical approach to the proof of existence of solutions for elliptic problems II
复制标题
证明椭圆问题解存在性的数值方法 II
DOI：
--
复制
发表时间：
1988
期刊：
影响因子：
--
通讯作者：
M. Nakao
中科院分区：
文献类型：
--
作者：
M. Nakao
本文是前面研究 ([2]) 的延续，其中我们利用 Schauder 不动点定理描述了计算机自动证明二阶狄利克雷问题弱解的存在性。我们使用类牛顿法和 Sadovskii 不动点定理为编码图新制定了一种验证方法。这种方法使我们能够消除先前工作中出现的算子谱半径的幅度限制。我们展示了一些数值示例，这些示例证实该方法确实适用于具有大谱半径的问题。
This paper is a continuation of the preceding study ([2]) in which we described an automatic proof by computer, utilizing Schauder’s fixed point theorem, of the existence of weak solutions for Dirichlet problems of second order. We newly formulate a verification method using the Newton-like method and Sadovskii’s fixed point theorem for the codensing map. This approach enables us to remove the magnitude limit of the spectral radius of operator appeared in the previous work. We show some numerical examples which confirm us that the method is really applicable to problems having large spectral radius.