Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 477-488 |
| Number of pages | 12 |
| Journal | Japan Journal of Applied Mathematics |
| Volume | 7 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1990 Oct |
| Externally published | Yes |
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Keywords
- boundary value problems
- error estimates
- finite element method
- fixed point theorem
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics
Cite this
A numerical approach to the proof of existence of solutions for elliptic problems II. / Nakao, Mitsuhiro T.
In: Japan Journal of Applied Mathematics, Vol. 7, No. 3, 10.1990, p. 477-488.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A numerical approach to the proof of existence of solutions for elliptic problems II
AU - Nakao, Mitsuhiro T.
PY - 1990/10
Y1 - 1990/10
N2 - 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.
AB - 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.
KW - boundary value problems
KW - error estimates
KW - finite element method
KW - fixed point theorem
UR - http://www.scopus.com/inward/record.url?scp=0000871632&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0000871632&partnerID=8YFLogxK
U2 - 10.1007/BF03167855
DO - 10.1007/BF03167855
M3 - Article
VL - 7
SP - 477
EP - 488
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
SN - 0916-7005
IS - 3
ER -