Numerical Differential Equations

Syllabus (Fall Semester, 2015)

Graduate School, Ewha Womans University


Course Number : MA 506

 

Class Hour : Wed 2/3 (9:30-12:15)

Hours and Credits : 3 hr 3 cr

 

Office Hour : Wed/Fri (2:00-2:45)

Instructor : Prof. June-Yub Lee

 

Office : SciCmplx A324(3277-3451)

E-mail : jyllee@ewha.ac.kr

 

http://math.ewha.ac.kr/~jylee


1. Main text book

Michael Celia(MIT/Princeton) and William Gray(Notre Dame), Numerical methods for differential equations, fundamental concepts for scientific and engineering applications. Prentice Hall. [PDE+FDM/FEM]


2. References


Robert Schilling and Sandra Harris(Clarkson), Applied numerical methods for engineers (using Matlab and C), Brooks/Cole, 2000. [Basic Numerical Tools]

John Strikwerda(Wisconsin), Finite Difference schemes and PDEs, Wadsworth & Brooks / Core, 1989. [Finite difference method]

Charles Hall and Thomas Porsching(Pittsburgh), Numerical Analysis of PDEs, Prentice Hall, 1990. [Finite element method / Analysis]

Tikhonov and Samarskii, Eqs of Mathematical physics, Dover, 1963(1990) [PDE]

Sobolev, PDEs of Mathematical physics, Dover, 1964(1989) [PDE]



3. Homeworks and Evaluation Scheme


- Homework or Computational Project : 4-5 times (40%)

- Final Examination : Theory and basic idea methods (60%)



4. Weekly Syllabus


강  의  주  제

강  의  제  목

교재

페이지

비 고

1-3

Partial differential equation

1.1 Physical systems

1.2 Defs and Eqs Properties

1.3 Characteristics and BC

1-43

8/31(M)

 

 

4-6

Finite difference approximation

(one-dimensional FDM)

2.1 Discrete approximations

2.3 Analysis of approximation

2.4 Generalized Formulation

2.6 Initial Value Problems

44-90

 

9/26-29(M)

 

7-8

Finite difference approximation

(Multi-dimensional FDM)

2.7 Multi-dimensional problems

2.8 Two dimensional examples

91-108

 

9

Midterm Exam Week

-

-

10/23-27(M)

10-12

Finite Element approximation

(Theoretical basis)

3.1 Weighted residuals

3.3 Computation Procedures

3.4 Mathematical requirements

114-165

 

13-14

Finite Element approximation

(Computational Methods)

3.5~3.6 Method of weighted residuals in 2D/3Ds

3.7 Galerkin Finite Element method

166-177

 

15

Miscellaneous Topics

4.3 Space-Time Discretization

242-254

 

16

Final Exam Week

Final (Written) Exam

-

12/14(M)

12/15-17(W)