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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王藹農 | |
| dc.contributor.author | Jhih-Ciang Wu | en |
| dc.contributor.author | 吳志強 | zh_TW |
| dc.date.accessioned | 2021-06-08T02:11:32Z | - |
| dc.date.copyright | 2016-02-16 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-01-22 | |
| dc.identifier.citation | [1] Vasile Berinde. Iterative approximation of fixed points for pseudo- contractive operators. In Seminar on Fixed Point Theory, volume 3, pages 209–216, 2002.
[2] Vasile Berinde. Iterative approximation of fixed points. Springer, 2007. [3] William E Boyce, Richard C DiPrima, and Charles W Haines. Ele- mentary differential equations and boundary value problems, volume 9. Wiley New York, 1992. [4] Ji-Huan He. A new approach to nonlinear partial differential equa- tions. Communications in Nonlinear Science and Numerical Simulation, 2(4):230–235, 1997. [5] Ji-Huan He. Variational iteration method–a kind of non-linear ana- lytical technique: some examples. International journal of non-linear mechanics, 34(4):699–708, 1999. [6] Ji-Huan He. Variational iteration method—some recent results and new interpretations. Journal of computational and applied mathematics, 207(1):3–17, 2007. [7] Ji-Huan He, Guo-Cheng Wu, and F Austin. The variational itera- tion method which should be followed. Nonlinear Science Letters A- Mathematics, Physics and Mechanics, 1(1):1–30, 2010. [8] Ji-Huan He and Xu-Hong Wu. Variational iteration method: new devel- opment and applications. Computers & Mathematics with Applications, 54(7):881–894, 2007. [9] SA Khuri and Ali Sayfy. Variational iteration method: Green’s functions and fixed point iterations perspective. Applied Mathematics Letters, 32:28–34, 2014. [10] Cornelius Lanczos. Linear differential operators, volume 564. SIAM, 1961. [11] Zhanjie Xu, James R Travis, and Wolfgang Breitung. Green’s function method and its application to verification of diffusion models of GAS- FLOW code. Forschungszentrum Karlsruhe, 2007. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/19653 | - |
| dc.description.abstract | 此篇論文主要在探討變換迭代法與固定點迭代之間的關聯性。變換迭代法是一種用來處理線性或非線性問題的解析技巧，我們將其與皮卡迭代法比較。另一方面，考慮非齊次常微分方程或者是非齊次偏微分方程，格林函數是一個相當好的解決技巧，在初始值問題中，我們利用此一函數的特性去推論我們所感到興趣的關聯性。本論文的結果可以應用在邊界值問題，更進一步地，在固定點迭代的選擇上也可以嘗試其他的迭代法。 | zh_TW |
| dc.description.abstract | The main aim of this article is to study the correlation between the variational iteration method and fixed-point iteration. The variational iteration method is an analytical technique for linear or non-linear problems and we compare it with one fixed-point iteration called Picard iteration. On the other hand, considering inhomogeneous ordinary differential equation or inhomogeneous partial differential equation, Green's function is a technique to solve these equations. We applied its special properties to deduce this correlation for initial value problems. Our result can be applied to boundary value problems. Furthermore, the selection of fixed-point iteration can be replaced. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T02:11:32Z (GMT). No. of bitstreams: 1 ntu-105-R02246001-1.pdf: 597664 bytes, checksum: 33f53297de1df26e2d7ffdaae4d5ce24 (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 致謝 i
Contents ii 中文摘要 iv Abstract v 1 Introduction 1 1.1 LiteratureReview......................... 2 2 Background 3 2.1 SomeFundamentals ....................... 3 2.1.1 HeavisideStepFunction ................. 4 2.1.2 DiracDeltaFunction................... 4 2.1.3 Green’sFunction ..................... 6 2.2 Fixed-pointIteration....................... 12 2.2.1 Fixed-point ........................ 12 2.2.2 PicardIteration ..................... 13 2.2.3 KrasnoselskijIteration.................. 14 2.2.4 MannIteration ...................... 14 3 VIM and Fixed-point iterative schemes 16 3.1 VariationalIterationMethod .................. 16 3.2 Relationship between the VIM and Standard Fixed-point It- erativeSchemes ......................... 17 3.2.1 FirstOrderDifferentialEquation . . . . . . . . . . . . 18 3.2.2 SecondOrderDifferentialEquation . . . . . . . . . . . 20 4 Conclusion 23 References 24 | |
| dc.language.iso | en | |
| dc.title | 藉由格林函數探討變換迭代法與固定點迭代之間的關聯性 | zh_TW |
| dc.title | Correlation between Variational Iteration Method and Fixed-point Iteration via Green's Function | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 謝春忠,陳中川 | |
| dc.subject.keyword | 格林函數,變換迭代法,固定點迭代, | zh_TW |
| dc.subject.keyword | Variational Iteration Method,Fixed-point Iteration, | en |
| dc.relation.page | 25 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2016-01-22 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
| 顯示於系所單位： | 應用數學科學研究所 | |
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