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課程名稱 |
數值偏微分方程
Numerical Partial Differential Equations |
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開課學期 |
108-2 |
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授課對象 |
理學院 應用數學科學研究所 |
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授課教師 |
薛克民 |
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課號 |
MATH7422 |
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課程識別碼 |
221 U6170 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期四3,4,5(10:20~13:10) |
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上課地點 |
天數430 |
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備註 |
總人數上限：12人
外系人數限制：5人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1082MATH7422_ |
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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 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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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. |
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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. |
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課程要求 |
(1) Introduction to differential equations (both ODEs and PDEs)
(2) Introduction to computational mathematics |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
Lecture notes given by A. Bergara on ``Finite difference numerical methods of partial differential equations in finance with Matlab'' (see bulletin board) |
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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) |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Term project 1 |
40% |
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2. |
Term project 2 |
60% |
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週次 |
日期 |
單元主題 |
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第1週 |
03/05 |
Course overview & finite-difference method for
2-point BVPs |
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第2週 |
03/12 |
Compact schemes for 2-point BVPs |
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第3週 |
03/19 |
Green's function & maximum-norm stability;
immersed boundary method & its variant for elliptic
problems with discontinuous coefficients |
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第4週 |
03/26 |
Numerical methods for heat equation |
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第5週 |
04/02 |
<font color=#ff0000> No class: 清明節補假</font> |
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第6週 |
04/09 |
Numerical methods for hyperbolic PDEs |
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第7週 |
04/16 |
Von Neumann analysis & stability of finite difference methods |
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第9週 |
04/30 |
<font color=#0000ff> Midterm project presentation </font> |
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第10週 |
05/07 |
Midterm project (sample solutions) |
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第11週 |
05/14 |
fractional step methods |
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第12週 |
05/21 |
exponential time differencing |
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第13週 |
05/28 |
Spectral methods |
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第14週 |
06/04 |
Integral equation method |
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第15週 |
06/11 |
Finite element methods |
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第16週 |
06/18 |
<font color=#0000ff> Final project presentation </font> |