The construction of wavelets and its application to the numerical analysis of differential equations
| Project/Area Number |
15K17597
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Matsue National College of Technology |
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Principal Investigator |
Fukuda Naohiro 松江工業高等専門学校, 数理科学科, 助教 (50736759)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | ウェーブレット / 数値解析 / fractional order |
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| Outline of Final Research Achievements |
As for the construction of wavelet, we succeeded to get fractional order wavelets and various types of wavelet. The construction of 4th order Stromberg wavelet with MRA and its Symlet types were investigated. As for the application to numerical analysis, we obtained some results, but there is room for improvement.
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| Academic Significance and Societal Importance of the Research Achievements |
ウェーブレット解析において，応用分野によって有効なウェーブレットに取り替えることは，より良い結果を得るために非常に重要である．そのため，たとえ小さな違いであっても，様々なウェーブレットを用いることが出来るという広い選択肢も持つことは応用面において価値が高い．本研究によって，既存のウェーブレットを組み合わせることにより，滑らかさなどの性質を目的に合わせて微調整し，新たなウェーブレットを構成できるようになった．
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Report
(5 results)
Research Products
(7 results)
