{"_buckets": {"deposit": "c72249e1-03ac-44d5-9e69-5ea86609e93e"}, "_deposit": {"id": "11241", "owners": [], "pid": {"revision_id": 0, "type": "depid", "value": "11241"}, "status": "published"}, "_oai": {"id": "oai:nagoya.repo.nii.ac.jp:00011241", "sets": ["681"]}, "author_link": ["34068", "34069", "34070", "34071", "34072", "34073", "34074", "34075", "34076", "34077", "34078", "34079", "34080", "34081"], "item_1618209983323": {"attribute_name": "助成情報", "attribute_value_mlt": [{"subitem_award_numbers": {"subitem_award_number": "11304004", "subitem_award_uri": "https://kaken.nii.ac.jp/ja/grant/KAKENHI-PROJECT-11304004"}, "subitem_award_titles": [{"subitem_award_title": "保存系の計算数理の総合的研究", "subitem_award_title_language": "ja"}], "subitem_funder_identifiers": {"subitem_funder_identifier": "https://doi.org/10.13039/501100001691", "subitem_funder_identifier_type": "Crossref Funder"}, "subitem_funder_names": [{"subitem_funder_name": "日本学術振興会", "subitem_funder_name_language": "ja"}]}]}, "item_19_biblio_info_6": {"attribute_name": "書誌情報", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "2002-03", "bibliographicIssueDateType": "Issued"}}]}, "item_19_description_4": {"attribute_name": "抄録", "attribute_value_mlt": [{"subitem_description": "時間発展に添って変動する現象の数理モデルを作り,対応する非線型常微分方程式を数値的に解き,表わしている現象をシミュレーションするとき,目標となる現象,特に理工学における現象のなかには,なんらかの保存則(conservation law)を内在し,保存則の再現が決定的な意味をもつ現象がしばしば見られる.典型的な例であるHamilton力学系では,エネルギー,symplectic構造,あるいは角運動量といった保存量が存在することが多く,むしろそうした保存量が力学系を特徴づけるということすら可能である.したがって,これらに対する計算も理想的にはやはり何らかの保存量をもつことが望まれ,あるいは保存量の再現がどの程度の正確さで可能であるかを知ることが,きわめて重要である.保存量の再現が,数値的安定性と緊密に結びついていることは論を俟たない. このことを念頭にして,非線型常微分方程式の離散近似解アルゴリズム全体の特性を解析し,保存系の観点に立って新たな解法設計の指針をうること,ならびにアルゴリズムの設計・実装にともなう問題点とその解決をめざして,分担者ならびに研究協力者の共同によって多彩な研究活動を展開し成果を収めた.たとえば Hamilton力学系の保存性およびその数値 解可積分な力学系の十分条件,積分を厳密に再現する離散解法の条件,逆にsymplectic数値解法による第一積分の非保存の条件,周期性を再現する Runge-Kutta-Nystrom schemeの条件などを明らかにした. 保存系に対する離散解法の並列化 Runge-Kutta法をaccross-the-stepの局所的なレベルで,あるいはWaveform Relaxationを通じて大域的なレベルで,並列化を進める観点で,その収束性能・並列化効率などを理論・実践の両面で明らかにした.また,それらの方法のプログラム化にも取り組んだ. などが挙げられ,さらに以下の項目についても成果を収めた. 変分原理に基づく保存的数値解法,離散近似解の精度保証,時間遅れあるいは確率的要素を含む微分方程式系の離散解法,破壊力学の数理研究成果は国内外の研究集会において発表されるとともに,学術論文としても多数が発表あるいは掲載予定である.", "subitem_description_language": "ja", "subitem_description_type": "Abstract"}]}, "item_19_description_5": {"attribute_name": "内容記述", "attribute_value_mlt": [{"subitem_description": "科学研究費補助金 研究種目:基盤研究(A)(1) 課題番号:11304004 研究代表者:三井 斌友 研究期間:1999-2001年度", "subitem_description_language": "ja", "subitem_description_type": "Other"}]}, "item_19_identifier_60": {"attribute_name": "URI", "attribute_value_mlt": [{"subitem_identifier_type": "HDL", "subitem_identifier_uri": "http://hdl.handle.net/2237/13113"}]}, "item_19_relation_40": {"attribute_name": "シリーズ", "attribute_value_mlt": [{"subitem_relation_name": [{"subitem_relation_name_text": "科学研究費補助金報告書;基盤研究(A)(1);11304004"}]}]}, "item_19_select_15": 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