課程名稱 |
數值偏微分方程 Numerical Partial Differential Equations |
開課學期 |
109-2 |
授課對象 |
理學院 數學研究所 |
授課教師 |
薛克民 |
課號 |
MATH7422 |
課程識別碼 |
221 U6170 |
班次 |
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學分 |
3.0 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期四3,4,5(10:20~13:10) |
上課地點 |
天數430 |
備註 |
總人數上限:12人 外系人數限制:5人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1092MATH7422 |
課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
課程大綱
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課程概述 |
Partial differential equations are of fundamental importance
in modeling many applications in science and technology.
Since in general it is difficult to find analytical solutions
for real-world problems, finding approximate solutions is necessary.
The goal of this course is to discuss various numerical approaches for the
construction of approximate solutions for ordinary and partial differential equations. |
課程目標 |
Both the analytical and computational tools will be emphasized in this course
in the hope to have a better understanding of the computed solutions as
well as the true solutions of the problems being solved. |
課程要求 |
(1) Introduction to differential equations (both ODEs and PDEs)
(2) Introduction to computational mathematics |
預期每週課後學習時數 |
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Office Hours |
另約時間 |
指定閱讀 |
待補 |
參考書目 |
1. Bertil Gustafsson, High Order Difference Methods for Time dependent PDE,
Springer 2008. (e-book)
2. Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial
Differential Equations, steady-state and time-dependent problems, SIAM 2007
(e-book)
3. Randall J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge 2002
4. Lloyd N. Trefethen, Spectral methods in Matlab, SIAM 2000
5. Journal papers (to be posted) |
評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
Term project 2 |
50% |
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2. |
Term project 1 |
50% |
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週次 |
日期 |
單元主題 |
第1週 |
02/25 |
Course overview |
第2週 |
03/04 |
2-point BVPs: finite-difference method, compact scheme, immersed interface method,
dispersion-relation preserving scheme |
第3週 |
03/11 |
Poisson solver |
第4週 |
03/18 |
Poisson solver |
第6週 |
04/01 |
<font color=#ff0000> No class: 溫書假</font> |
第7週 |
04/08 |
von Neumann stability analysis for initial-value problems |
第8週 |
04/15 |
Runke-Kutta (RK) methods for IVP of ODEs |
第9週 |
04/22 |
Runge-Kutta-Chebyshev (RKC) method |
第10週 |
04/29 |
<font color=#0000ff> Term project presentation </font> |
第11週 |
05/06 |
Midterm project: Numerical solutions for sample time-dependent problems |
第12週 |
05/13 |
Interface sharping method for hyperbolic problems |
第13週 |
05/20 |
Exponential time differencing methods for PDEs |
第14週 |
05/27 |
Relaxation models and schemes |
第15週 |
06/03 |
Spectral methods for PDEs |
第17週 |
06/17 |
<font color=#0000ff> Final project presentation </font> |
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