This paper presents an improved method for determining the invertibility of second-order linear elliptic operators with a bound on the norm of their inverses by computers in a mathematically rigorous sense. This approach is an improvement on a previous method (Nakao et al. in Jpn J Ind Appl Math 32:19–32, 2015) which used a projection and constructive a priori error estimates. Several examples confirming the effectiveness of the proposed procedure are reported.
|ジャーナル||Japan Journal of Industrial and Applied Mathematics|
|出版ステータス||出版済み - 7 1 2019|
All Science Journal Classification (ASJC) codes
- Applied Mathematics