Numerical Differential Equations
數值微分方程

Fall 2008


Jinn-Liang Liu

高雄大學應數系

 

Exam 2. (On 1/6/09)

Projects. (Final due on 12/30)

No projects will be accepted after this day.

Project 2. (Due on 12/23)
Do Project 7.1 (CG) in Lecture 7.

Homework 3. (Due on 12/16)
Do Problems 7.5 and 8.1~8.2.

Homework 2. (Due on 11/25)
Do Problems 6.1~6.4 and 7.1~7.4.

Exam 1. (On 11/11)

Project 1. (Due on 10/28)
Do Project 3.1 (JM) in Lecture 3. 

Homework 1. (Due on 10/14)
Do Problems 2.1 and 2.2 in Lecture 2.

課程大綱

Lecture 1.  1D Poisson's Equation and Finite Difference Method (FDM)   

Lecture 2.  Gaussian Elimination (GE) for Ax=b  

Lecture 3.  Jacobi’s Method (JM)

Templates for the Solution of Linear Systems   (pdf)

Lecture 4.  Gauss-Seidel Method (GS)    

Lecture 5.  Successive Overrelaxation Method (SOR)   

Lecture 6.  Symmetric Successive Overrelaxation Method (SSOR)  

Lecture 7.  Conjugate Gradient Method (CG)  

Lecture 8.  Finite Element Method (FEM) for 1D Poisson’s Problem   

Lecture 9.  2D and 3D Poisson's  Equation

Lecture 10.  Convection-Diffusion-Reaction Model  

 

教學目標

·         Learn basic numerical methods for Partial Differential Equations (PDEs)

·         Learn basic numerical methods in Numerical Linear Algebra

·        Learn basic Physics behind PDEs

·        Learn programming in scientific computing

授課方式

·        Regular Lecturing

評分標準

·        Programming projects 30%

·        Homeworks 40%

·        Exams 30%

教科書

·        Jinn-Liang Liu, Lecture Notes on Numerical Methods for Partial Differential Equations, 2008. 

閱讀文獻

·        R. J. LeVeque, Finite Difference Methods for Differential Equations, 2005. LeVeque-FDM-2005.pdf
(Chapters 1-5)

·      E. Suli, Finite Element Methods for Partial Differential Equations, 2007. Suli-FEM-2007.pdf

·      G. H. Golub and C. F. Van Loan, Matrix Computations, Johns Hopkins University Press, 1996.

·      A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations, Springer-Verlag, 1994.

·      R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra , V. Eijkhout, R. Pozo, C. Romine, and H. Van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition, SIAM, 1994, Philadelphia, PA.
Templates for the Solution of Linear Systems   (pdf)

·      J. R. Shewchuk, An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, 1994.