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Please use this identifier to cite or link to this item: http://ir.ncue.edu.tw/ir/handle/987654321/15821

Title: 非線性拋物方程式的可調適網格解
Adaptive Solutions of Nonlinear Parabolic Equations with Sharp Peaks
Authors: 周忠強
Contributors: 數學系
Keywords: 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
Date: 2000
Issue Date: 2013-03-12T04:08:40Z
Publisher: 行政院國家科學委員會
Abstract: 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.
Relation: 國科會計畫, 計畫編號: NSC89-2115-M018-013; 計畫期間: 8808-8907
Appears in Collections:[數學系] 國科會計畫

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