{"_buckets": {"deposit": "fff323c1-a347-4ab1-a11d-96705099d94c"}, "_deposit": {"id": "11206", "owners": [], "pid": {"revision_id": 0, "type": "depid", "value": "11206"}, "status": "published"}, "_oai": {"id": "oai:nagoya.repo.nii.ac.jp:00011206", "sets": ["681"]}, "author_link": ["33901", "33902", "33903", "33904", "33905", "33906", "33907", "33908", "33909", "33910", "33911", "33912", "33913", "33914", "33915"], "item_1618209983323": {"attribute_name": "助成情報", "attribute_value_mlt": [{"subitem_award_numbers": {"subitem_award_number": "08304016", "subitem_award_uri": "https://kaken.nii.ac.jp/ja/grant/KAKENHI-PROJECT-08304016"}, "subitem_award_titles": [{"subitem_award_title": "発展系の数値解析の総合的研究", "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": "1999-03", "bibliographicIssueDateType": "Issued"}}]}, "item_19_description_4": {"attribute_name": "抄録", "attribute_value_mlt": [{"subitem_description": "本研究課題は,理工学の多くの分野で現われる時間発展をともなう現象を数理科学における発展系としてモデル化し,これを解法特に離散近似解法の観点で総合的に検討し,新たな結果をえようとするものである.分担者および多数の研究協力者の研究推進によって,以下の成果をうることができた. 時間遅れあるいは確率的要素を含む発展系の離散解法 解折的な漸近安定性に対応する数値的安定性をもつ離散変数法を系統的に研究し,主として線型安定性に関する結果と,一部非線型安定性についても成果をえ, その解析と実際への応用を展開することができた. 力学系に対する長時間離散積分法 Hamilton力学系とそれに応ずるsymplectic numerical integratorsの代数的な関係を明らかにするとともに,さらに保存量と,の関係も解明することができた. 離散近似解の精度保証 放物型発展系に対する有限要素法に基づく精度保証を,大きく前進させるとともに,常微分方程式系に関しても従来の方法を改善することができた. 発展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WaveformRe-laxationを通じて大域的なレベルで,並列化を進める観点で,その収束性能などを理論・実践の両面で明らかにした. 発展系に対する高性能かつ安定な離散解法の開発と評価 時間方向の数値積分を離散化する際に,微分方程式の定義函数の導函数を取り入れるなど,多くの工夫による新しい試みを導入し,解析することができた. 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