Numerical Differential Equations
Syllabus (Fall Semester, 2012)
Graduate School, Ewha Womans University
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Course Number : MA 506 |
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Class Hour : Thur 2-3(9:30-12:15) |
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Hours and Credits : 3 hr 3 cr |
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Office Hour : Mon 5(2:00-) |
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Instructor : Prof. June-Yub Lee |
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Office : SciCmplx A320(3277-3451) |
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E-mail : jyllee@ewha.ac.kr |
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http://math.ewha.ac.kr/~jylee |
1. Text book and References
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]
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]
2. Homeworks and Evaluation Scheme
- Homework or Computational Project : 4-5 times (40%)
- Final Examination : Theory and basic idea methods (60%)
3. Weekly Syllabus
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주 |
강 의 주 제 |
강 의 제 목 |
교재 페이지 |
비 고 |
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1-3 |
Partial differential equation |
1.1 Physical systems 1.3 Characteristics and BC |
1-43 |
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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 |
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7 |
Finite difference approximation (Multi-dimensional FDM) |
2.7 Multi-dimensional problems 2.8 Two dimensional examples |
91-108 |
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8 |
Midterm Exam |
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9-11 |
Finite Element approximation (Theoretical basis) |
3.1 Weighted residuals 3.3 Computation Procedures 3.5 Method of weighted residuals |
114-165 |
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12-13 |
Finite Element approximation (Computational Methods) |
3.7 Galerkin Finite Element method |
166-177 |
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14 |
Miscellaneous Topics |
4.3 Space-Time Discretization |
242-254 |
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15 |
Final Exam |
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