1. | Introduction | Introduction | ||
Introduction | Introduction | |||
2. | Finite Difference Approximation | Approximation for derivative and its truncation error | ||
3. | FDM for steady state Heat equation | 1. Heat equation 2. FDM for Steady state heat equation 3. FDM for various boundary condition. |
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FDM for steady state Heat equation | 1. Heat equation 2. FDM for Steady state heat equation 3. FDM for various boundary condition. |
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4. | Existence and uniqueness of heat equation. | Existence and Uniqueness for pure- Neumann condtion | ||
5. | FDM for 2D steady state Heat equation | 1. Global Error 2. The 2-dimensional Steady-state Heat Eq. 3. Singular perturbation and boundary layers 4. Initial Value Problem for ODE |
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FDM for 2D steady state Heat equation | 1. Global Error 2. The 2-dimensional Steady-state Heat Eq. 3. Singular perturbation and boundary layers 4. Initial Value Problem for ODE |
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6. | Advection Equation and ODE | 1. Advection Equation and its solution 2. Duhamels priciple 3. Lipschitz Continuity 4. Existence of solution of ODE |
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7. | FDM for Ordinary Differential Equation(ODE) | 1. One-step method 2. Multistep method(LMN) 3. Comparison between One-step and Multi step method 4. Zero-Stability |
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FDM for Ordinary Differential Equation(ODE) | 1. One-step method 2. Multistep method(LMN) 3. Comparison between One-step and Multi step method 4. Zero-Stability |
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8. | Stability for FDM | 1. Zero-stability 2. Absolute-stability |
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9. | Absolute Stability and its region | 1. Absolute statbility 2. Stability region for linear multistep method 3. Plotting Stability region 4. Diffusion Equation and Parabolic equation. |
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Absolute Stability and its region | 1. Absolute statbility 2. Stability region for linear multistep method 3. Plotting Stability region 4. Diffusion Equation and Parabolic equation. |
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10. | Stability and Convergency for diffusion equation. | Stability analysis by eigen values | ||
11. | Diffusion Equation | 1. Convergence 2. Lax Equivalence Theorem 3. Von Neumann analysis 4. FDM for heat equation. 13분 30초 까지 음성 없음. |
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Diffusion Equation | 1. Convergence 2. Lax Equivalence Theorem 3. Von Neumann analysis 4. FDM for heat equation. |
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12. | Review for Midterm exam. | |||
13. | FDM for advection equation. | 1. Method of lines discretization(MOL) 2. Lax-Friedrichs (LxF) 3. Lax-Wendroff (LxW) 4. Upwind |
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FDM for advection equation. | 1. Method of lines discretization(MOL) 2. Lax-Friedrichs (LxF) 3. Lax-Wendroff (LxW) 4. Upwind |
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14. | Von Neumann analysis for LxF, LxW, Upwind, etc | 1. 폰노이만 분석 2. Lax-Friedrichs 3. Lax-Wendroff 4. Upwind |
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15. | FVM (1) | 1. Conservation Law 2. General formulation 3. Numerical Flux |
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FVM (1) | 1. Conservation Law 2. General formulation 3. Numerical Flux 34분 이후로 음성 없음. |
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16. | FVM (2) | 1. CFL Condition 2. Flux formulation |
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17. | FVM (3) - Numerical Fluxes | 1. Lax-Friedrichs 2. Richmyer method 3. Upwind method 4. Godunovs method 5. High - Resolution Mthods 6. Limiters |
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FVM (3) - Numerical Fluxes | 1. Lax-Friedrichs 2. Richmyer method 3. Upwind method 4. Godunovs method 5. High - Resolution Mthods 6. Limiters |
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18. | FVM (4) | 1. Limiters 2. TVD |
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19. | FVM (5) - Limiters | 1. Superbee limiter 2. Flux Limiters 3. Harten Theorem 4. FVM in n-dimensional space |
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FVM (5) - Limiters | 1. Superbee limiter 2. Flux Limiters 3. Harten Theorem 4. FVM in n-dimensional space |
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20. | FEM (Finite Element Mthod) (1) | 1. Introduction 2. Weak Derivatives 3. Sobolev Spaces |
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FEM (Finite Element Mthod) (1) | 1. Introduction 2. Weak Derivatives 3. Sobolev Spaces |
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21. | FEM (2) | 1. General spaces 2. Approximations |
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22. | FEM (3) | 1. Weak forms 2. Useful Theorems for FEM 3. Greens formula |
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FEM (3) | 1. Weak forms 2. Useful Theorems for FEM 3. Greens formula |
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23. | FEM (4) | 1. Formulation for FEM 2. Reference triangle |
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24. | FEM (5) | Trace Thoerem, Sobolev Embedding | ||
FEM (5) | Trace Thoerem, Sobolev Embedding |