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題名 | 一維變係數且非齊次微分方程式於有限差分法中修正項之探討=The Exploration of Correctionterm in the One-Dimensional Non-Homogeneous Advection-Diffusion Equation with Variable Coefficient |
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作者 | 郭鴻森; 李志良; Kou, Hong-sen; Lee, Chi-liang; |
期刊 | 大同學報 |
出版日期 | 19961100 |
卷期 | 26 1996.11[民85.11] |
頁次 | 頁205-211+416 |
分類號 | 446.8 |
語文 | chi |
關鍵詞 | 一維; 變係數; 非齊次微分方程式; 有限差分法; 修正項; |
中文摘要 | 本研究以一維含變係數及非齊次之advection-diffusion equation為例,應用有限差分法運算時,利用修正項來降低截斷誤差的階數。本研究方法首先推導有限差分通式,此通式可清楚表示出各階導數之截斷誤差,將其代入統御方程式後,為了消除各階截斷誤差,而推導出非齊次項於有限差分法運算時所需之修正項,且修正項是依所消除之各階截斷誤差而伴隨產生。經數值計算結果顯示,本研究所推導出之修正項的確有補正誤差且提昇準確度的效果,若修正項為無限多個,則可依準確度之要求補回修正項,如此便可得到高準確度數值解。 |
英文摘要 | The one-dimensional non-homogeneous advection-diffusion equation with variable coefficient is solved by finite difference method where the correction terms are proposed in this study to reduce the order of truncation error. First, the present study derives a general form which can show finite difference formulas and truncation error for each derivative. Using the generalized finite difference formulas into the governing equation, the correction terms are generated when eliminate each order of truncation error. The results show that the correction terms are useful to increase the accuracy of numerical solution. The more accurate solution can be obtained by inducing higher order of correction term. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。