|
課程名稱 |
數值偏微分方程式一
Numerical Partial Differential Equations (Ⅰ) |
|
開課學期 |
104-2 |
|
授課對象 |
理學院 應用數學科學研究所 |
|
授課教師 |
薛克民 |
|
課號 |
MATH7409 |
|
課程識別碼 |
221 U1310 |
|
班次 |
|
|
學分 |
3 |
|
全/半年 |
半年 |
|
必/選修 |
選修 |
|
上課時間 |
星期二8,9(15:30~17:20)星期四5(12:20~13:10) |
|
上課地點 |
天數102天數102 |
|
備註 |
總人數上限：80人 |
|
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1042MATH7409_npde |
|
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.
The topics to be covered in the course can be found in Ceiba's 大綱內容.
|
|
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 solutions of original problems.
|
|
課程要求 |
Prerequisite:
(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 JLeVeque, Finite Difference Methods for Ordinary and Partial
Differential Equations, steady-state and time-dependent problems, SIAM 2007.
(e-book) |
|
評量方式
(僅供參考) |
|
No. |
項目 |
百分比 |
說明 |
|
1. |
Homework |
50% |
|
2. |
Term project proposal |
10% |
Topic of the term project should be taken from either (1) the one proposed in the class, or
(2) the one proposed by you with consent from the instructor. A proposal for the term project needs to be submitted before April 14, 2016, and a 5-10mins presentation should be given in week 8 in class. |
3. |
Term project report |
40% |
A written report should be handed in for the proposed project before June 16, 2016 that consist of the following components: (1) Introduction: problem of interests, (2) Solution methods, (3) Results, and (4) Scientific significances. |
|
|
週次 |
日期 |
單元主題 |
|
第1週 |
2/23,2/25 |
Overview &
2-point boundary value problems: Finite difference approach |
|
第2週 |
3/01,3/03 |
2-point BVPs: High-order finite difference schemes |
|
第3週 |
3/08,3/10 |
Poisson-type equation: High-order finite difference method |
|
第4週 |
3/15,3/17 |
Poisson's solver in disk & compact schemes |
|
第5週 |
3/22,3/24 |
Dispersion-Relation-Preserving schemes &
numerical methods for IVPs for ODEs |
|
第7週 |
4/07 |
Integral equation methods for elliptic PDEs |
|
第9週 |
4/19,4/21 |
Initial value problems of ODEs: multi-stage and multi-step methods |
|
第11週 |
5/03,5/05 |
Finite difference methods for parabolic PDEs |
|
第13週 |
5/17,5/19 |
Finite-difference and finite-volume methods for hyperbolic PDEs |
|
第16週 |
06/07 |
出國開會停課 |
|
第18週 |
06/23 |
Term project report due |
|
第8-2週 |
04/14 |
Term project proposal presentation |
|