2015 Fiscal Year Final Research Report
Implementation and extension of ``look-ahead'' linear multistep methods for ODEs
Project/Area Number |
24540150
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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Research Institution | Doshisha University |
Principal Investigator |
Mitsui Taketomo 同志社大学, 研究開発推進機構, 嘱託研究員 (50027380)
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Co-Investigator(Renkei-kenkyūsha) |
ESAKI Nobuyuki 豊田工業高等専門学校, 准教授 (80311033)
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Project Period (FY) |
2012-04-01 – 2016-03-31
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Keywords | 数値解析 / 微分方程式 / 離散変数法 / 収束性 / 安定性 / 性能評価 |
Outline of Final Research Achievements |
We proposed the ``look-ahead'' linear multistep methods (LALMM), a new class of discrete variable methods solving initial-value problems of ordinary differential equations, gave analysis of their order of convergence as well as of stability and derived several LALMM of two steps, whose implementation and performance evaluation were carried out. Our results showed that the new schemes of LALMM are competitive with the conventional methods like as the classical Runge-Kutta method. Our study suggested more well-performing LALMM can be derived by increasing its number of steps can be introduced and extended to apply to other functional equations closely related to ordinary differential equations.
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Free Research Field |
数値解析
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