2020 Fiscal Year Final Research Report
Numerical verification method of solutions for evolutionary equations by applying the matrix exponential
Project/Area Number |
17K17948
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Foundations of mathematics/Applied mathematics
Computational science
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Research Institution | Saga University |
Principal Investigator |
Kimura Takuma 佐賀大学, 理工学部, 准教授 (60581618)
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Project Period (FY) |
2017-04-01 – 2021-03-31
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Keywords | 精度保証付き数値計算法 / 微分方程式 / 有限要素法 / 発展方程式 / 数値計算 |
Outline of Final Research Achievements |
In this research, we studied some numerical verification methods for a full discrete solution of the evolutionary partial differential equations. Proposed methods are based on the error estimates of finite element semidiscretization in space direction combined with an interpolation in time that uses the fundamental solution (represented by the exponential of matrix) for the semidiscretized problem.
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Free Research Field |
数値解析
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Academic Significance and Societal Importance of the Research Achievements |
計算機を用いた数値計算は非常に有用であるが,一般に,そこで得られる数値解は誤差を含む.そのため,数値解の精度を厳密に保証できる数値計算手法が近年活発に研究されている. 本研究の主な成果は,いくつかの条件が整えば発展方程式の数値解に対する誤差評価を与えるというものであり,与えられた問題の解の存在範囲もしくは一意存在の範囲を計算機を用いて自動的に求める精度保証付き数値計算法の開発に寄与する成果といえる.
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