Announcements ,  Course Information ,  Outline ,  Homework ,  Matlab Tutorial ,  Internet Resources

 

Announcements:

1/22:報告順序:

• Image Processing: Denoise by 朱書賢. 投影片及程式
• Reaction Diffusion by 林威溢和胡凱揚. 投影片及程式
• Discontinuous Solution to the advection equation by 陳銚壬. 投影片及程式
• Dispersion and dissipation by 龐詩倩. 投影片(powerpoint)
• High order difference methods for wave equations by 邱垂青. 投影片及程式
• Discontinuous Galerkin methods for Laplace's equation by 柯承頤.投影片; 程式

1/21:Project presentation:時間: 1/22, 2pm-5pm; 地點:4F 電腦室; 請同學先將報告檔案及程式(若想讓其他同學執行的話)寄給我
1/?:Sample code for advection equation:Sample.zip
12/24: 作業二,三修正
11/29: Possible Project problems:

• Diffusion Equation with a source term.
• Diffusion Equation with time varying boundary conditions
• Reaction-Diffusion Equation: 參考資料
• Advection-Diffusion Equation: Stability issue
• Advection- Equation with time varying boundary conditions
• Liner Hyperbolic System

10/11:

• 更新 Example1.tex , ex4.m .
• ex4.m執行後會在同一目錄內產生三個檔: ex1.eps (Error-h 圖), ex1.txt(數值解誤差及rate of convergence), ex1.tex (ex1.txt 的 latex table寫法).
• 欲嘗試Latex者:
• 可將example1.tex暫存於系上電腦使用者目錄,
• 再將ex1.eps及ex1.tex複製至C:/xtemp.
• 開啟Winedt, 先執行cwtex, 再執行Latex, 最後以dvi看結果.

10/11: 上傳 Sample Code (含本週上課範例程式).
10/11: Example1.tex
10/8: Homework 1 (Due 10/25).
10/1:增加 Numerical Computing with MATLAB 的連結(於Internet Resources), 對Matlab不熟悉的同學可以下載參考.
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Elementary Numerical Partial Differential Equations:
Finite Difference Methods

Time and Place: Tue. 15:10-17:00; Thu. 10:10-11:00, Math 3177
Lecturer: Min-Hung Chen
Office: Math Building Rm. 404; Ph. 2757575 Ext 65127
e-mail: mhchen@math.ncku.edu.tw
Web: www.math.ncku.edu.tw/~mhchen
Prerequisite: Calculus, Linear Algebra.
Text: Finite Difference Methods for Differential Equations by Randall J. LeVeque
References:

• Time Dependent Problems and Difference Methods by Bertil Gustafsson, Heinz-Otto Kreiss and Joseph Oliger
• Finite Difference Schemes and Partial Differential Equations by John Strikwerda

Grades will be based upon: Homework and in-class participation
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OUTLINE:

• Estimating errors in numerical solutions
• Introduction to Matlab
• Finite Difference Approximation
• Boundary Value Problems
• Elliptic Equations
• Initial Value Problem for ODE's
• Some basic PDEs
• Fourier Analysis of Linear PDEs
• Diffusion Equations
• Advection Equations

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Homework

• Homework 1 (Due 10/25).
• Homework 2 (Due 1/24).
• Homework 3 (Due 1/24).

Old Homework (2006). 僅供參考

• Homework 1.
• Homework 2, Sample code (zip file).
• Homework 3.
• Homework 4, Sample code (zip file).
• Burgers Equation: Sample code (zip file).

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Matlab tutorial

Sample Code:
• test.m
• ex1.m, ex2.m , ex3.m, ex4.m
• fun.m, dfun.m , d2fun.m
• Sample.zip

• Matlab tutorial (postscript file), (pdf file)
• tutorial.tar, tutorial.rar, tutorial.zip,

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Internet Resources

Numerical Computing with MATLAB

Flaherty's Course Notes : Computational Linear Algebra, ODE, PDE, Finite Element Analysis.

Website of Douglas Arnold:
     Lecture Notes (Numerical Analysis), Some disasters attributable to bad numerical computing

Website of Yousef Saad: Iterative methods for sparse linear systems

Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations by Lloyd N. Trefethen

Website of Randall J. LeVeque:  Lecture Notes of "Finite Difference Methods for Differential Equations"(ps.gz)

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