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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 |
111-2 |
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授課對象 |
理學院 大氣科學系 |
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授課教師 |
陳宜良 |
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課號 |
AtmSci5101 |
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課程識別碼 |
229 U5950 |
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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 |
星期四9(16:30~17:20)星期五8,9(15:30~17:20) |
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上課地點 |
大氣A104大氣A104 |
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備註 |
總人數上限：20人 |
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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 for real-world problems, and finding
numerical solutions is necessary. Roughly speaking, there are three classes of numerical PDE
methods: finite difference methods, finite element methods and spectral methods. In this course,
we will cover the basic concepts of all these methods for elliptic equation, parabolic equation,
hyperbolic equation, and convection-diffusion equations. Algorithms and some stability theory
will be introduced. Applications to atmospheric science will be discussed.
‧ Chapter 1. Numerical ordinary differential equations
‧ Chapter 2. Finite difference methods for linear parabolic equations
‧ Chapter 3. Finite difference methods for elliptic equations
‧ Chapter 4. Finite difference methods for hyperbolic equations
‧ Chapter 5. Finite element methods for elliptic equations in general domains
‧ Chapter 6. Spectral methods for parabolic equations.
. Chapter 7. Selected topics in computational fluid dynamics |
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課程目標 |
The goal is to provide basic knowledge for students to be able to read and implement
some research papers of numerical partial differential equations with applications. |
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課程要求 |
Prerequisite: Multivariable Calculus, basic ODE and PDE., and any programming language: one of Matlab or Python or C++.
Finish 5-6 projects. |
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預期每週課後學習時數 |
6 hours + |
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Office Hours |
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指定閱讀 |
I-Liang Chern, Lecture note on numerical PDEs
Chi-Wang Shu, Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws, ICASE report. |
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參考書目 |
‧ RandyLeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations,
steady-state and time-dependent problems, SIAM 2007
‧ Mats G. Larson, Fredrik Bengzon The Finite Element Method: Theory, Implementation,
and Applications
‧ David A. Kopriva Implementing Spectral Methods for Partial Differential Equations
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評量方式
(僅供參考) |
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針對學生困難提供學生調整方式 |
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上課形式 |
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作業繳交方式 |
書面報告取代口頭報告, 口頭報告取代書面報告 |
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考試形式 |
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其他 |
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週次 |
日期 |
單元主題 |
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第1週 |
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Numerical ODEs
• Finite differencing
• Basic ODE solver
• Runge-Kutta methods
* Multistep methods
* Stability and convergence |
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第2週 |
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Finite Difference methods for heat equation (design, stability, error analysis)
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