Enclosures of solution curve of differential equations by computer-assisted proof
Project/Area Number |
21540134
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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Research Institution | Kyushu University |
Principal Investigator |
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Co-Investigator(Renkei-kenkyūsha) |
NAGATOU Kaori 九州大学, マス・フォア・インダストリ研究所, 准教授 (40326426)
|
Project Period (FY) |
2009 – 2011
|
Project Status |
Completed (Fiscal Year 2011)
|
Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
Keywords | 計算機援用証明 / 精度保証付き数値計算 / 非線形偏微分方程式 / 非線形微分方程式 / 解曲線の追跡 / 線形化作用素の可逆性 / 無限次元Newton法 / 陰関数定理 / 固有値問題 / 解の存在検証 / 非自己共役固有値問題 / 固有値の除外 / 線形化作用素のノルム評価 |
Research Abstract |
We developed a computer-assisted theory to verify the existence of the solutions for nonlinear elliptic boundary value problems with local uniqueness. We also proposed verified computations of eigenvalue exclosures for the linearization problems. Finally combining with developed method and the implicit function theorem, we introduced a procedure to enclose solution curves of nonlinear partial differential equations by computer-assisted proof and confirmed its effectiveness by some verified results.
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Report
(4 results)
Research Products
(59 results)