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課程名稱 |
數值偏微分方程式一
NUMERICAL PARTIAL DIFFERENTIAL EQUATIONS(I) |
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開課學期 |
99-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
薛克民 |
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課號 |
MATH7409 |
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課程識別碼 |
221 U1310 |
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班次 |
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學分 |
3 |
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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 |
星期二6,7,8(13:20~16:20) |
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上課地點 |
新303 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/991npde |
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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 in modeling natural phenomena.However, it is difficult to find analytical solutions in general
for real-world problems and finding numerical solutions is necessary.
Finite difference methods are basic numerical methods for solving partial differential equations.
Part I: Boundary Value Problems
1. Finite difference approximations,
2. Finite difference methods for elliptic equations,
3. Iterative solvers,
Part II: Time-Dependent Problems
4. Numerical ordinary differential equations
5. Stability and convergence
6. Diffusion equations
7. Hyperbolic equations.
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課程目標 |
The goal of this course is to provide basic theory and computational skills. |
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課程要求 |
Calculus, Introduction to Ordinary Differential Equations, Introduction to Partial Differential Equations, Introduction to Computational Mathematics.
You are also required to know C or matlab. If you are not familiar with these basic tools, you may still take this course with self study of these programming skills.
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預期每週課後學習時數 |
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Office Hours |
每週一 11:00~12:00 |
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指定閱讀 |
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參考書目 |
Randy LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, steady-state and time-dependent problems, SIAM 2007.
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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. |
Homework |
40% |
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2. |
Computational test |
30% |
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3. |
Written test |
30% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/14 |
Calculation of weights in finite difference formulas |
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第2週 |
9/21 |
Finite difference approximation & two-point boundary value problems |
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第3週 |
9/28 |
Poisson solver & its faster version |
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第4週 |
10/05 |
Poisson's problems with discontinuous coefficients: Immersed interface methods & the variants |
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第5週 |
10/12 |
No class (travel abroad for a conference) |
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第6週 |
10/19 |
Poisson's problems in non-rectangular domains: Mapped grid approach & the others |
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第7週 |
10/26 |
Numerical methods for IVPs of ODEs |
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