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An Explicit Form of the Minimum Eigenvalue of the One-Dimensional Heat Equation
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- Arai Kazuo
- Kawasaki Steel Corporation
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- Marui Tomohiro
- Kawasaki Steel Corporation
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- Maruyama Satosi
- Kawasaki Steel Corporation
Bibliographic Information
- Other Title
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- 1次元熱拡散方程式の最小固有値を求める閉じた計算式
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Description
This note presents a practical approximation method for computing the minimum eigenvalue for a transcendental equation derived from the heat equation with a convective boundary condition. The transcendental equation is approximated by a finite continued fraction equation, which is a quadratic equation. Its solution(the minimum eigenvalue ) is obtained in a closed form depending explicitly on the Biot number. The method is faster than the conventional Newton method and the error is within 0.3%, a level that is quite satisfactory for practical use.
Journal
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- Transactions of the Japan Society for Industrial and Applied Mathematics
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Transactions of the Japan Society for Industrial and Applied Mathematics 2 (3), 169-175, 1992
The Japan Society for Industrial and Applied Mathematics
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Details 詳細情報について
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- CRID
- 1390282680744212992
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- NII Article ID
- 110001883523
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- NII Book ID
- AN10367166
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- ISSN
- 24240982
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- Text Lang
- ja
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- Data Source
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- JaLC
- CiNii Articles
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- Abstract License Flag
- Disallowed
