Numerical Differential Equations

Syllabus (Fall Semester, 2017)

Graduate School, Ewha Womans University


Course Number : MA 506

 

Class Hour : Tuesday (9:30-12:15)

Hours and Credits : 3 hr 3 cr

 

Office Hour : Thursday (2:00-3:00)

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

(9/5,
12,19)

Partial differential equation

1.1 Physical systems

1.2 Defs and Eqs Properties

1.3 Characteristics and BC

1-43

 

4-6

(9/26,

10/10)

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

10/3-9(추석)

7-8

(10/17, 10/24)

Finite difference approximation

(Multi-dimensional FDM)

2.7 Multi-dimensional problems

2.8 Two dimensional examples

91-108

 

9

-

Review

-

 

10-12

(11/7, 14,21)

Finite Element approximation

(Theoretical basis)

3.1 Weighted residuals

3.3 Computation Procedures

3.4 Mathematical requirements

114-165

 

13-14

(11/28,12/5)

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

(12/12)

Miscellaneous Topics

4.3 Space-Time Discretization

242-254

 

16

Final Exam Week

Final (Written) Exam

-

12/19(Tues)