|
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 |
|
|
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 |
|
|
核心能力關聯 |
本課程尚未建立核心能力關連 |
|
課程大綱
|
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
|
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 |
|
|
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% |
|
2. |
Term project 1 |
50% |
|
|
|
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> |
|