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請使用永久網址來引用或連結此文件:
http://ir.ncue.edu.tw/ir/handle/987654321/15821
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題名: | 非線性拋物方程式的可調適網格解 Adaptive Solutions of Nonlinear Parabolic Equations with Sharp Peaks |
作者: | 周忠強 |
貢獻者: | 數學系 |
關鍵詞: | 預測-修正法;拋物方程式;收斂性分析;可調適網格點 Predictor-Corrector Method;Parabolic Partial Differential Equations;Analysis of Convergence;Adaptive Grids |
日期: | 2000
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上傳時間: | 2013-03-12T04:08:40Z
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出版者: | 行政院國家科學委員會 |
摘要: | 在此成果報告,我們運用到"預測-修正法"在一可調適網格點上解一維非線性拋物方程式,三個主要結果在此保告呈現。首先,在兩個典型例子的測試,我們發現"預測-修正法"比" 顯示差分法"表現好地非常多;第二,對於現性拋物方程式的非一致式網格解的收斂性分析,"預測-修正法"比"標準差分法"放寬許多閜設條件;最後,在測試的非線性問題上,我們的演算法表現很良好。 A predictor-corrector method on adaptive grids for one-dimensional parabolic problems is developed in this report. Three issues are investigated for the algorithm. First,we heuristically show that a predictor-corrector method performs much better than explicit difference method by testing on two typical nonlinear examples on uniform grids. Second, comparing with standard finite ifference methods on the analysis of convergence for linear parabolic equations on nonuniform grids, we have found that the predictor-corrector method relaxes more conditions on its assumption. Third, the algorithm performs well on the testing suite. |
關聯: | 國科會計畫, 計畫編號: NSC89-2115-M018-013; 計畫期間: 8808-8907 |
顯示於類別: | [數學系] 國科會計畫
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2020101812003.pdf | 150Kb | Adobe PDF | 355 | 檢視/開啟 |
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