# ## 주메뉴

### 수치 편미분 방정식

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자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
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2012년 2학기
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Introduction #### 차시별 강의      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 equation2. FDM for Steady state heat equation3. FDM for various boundary condition.  FDM for steady state Heat equation 1. Heat equation2. FDM for Steady state heat equation3. FDM for various boundary condition. 4. Existence and uniqueness of heat equation. Existence and Uniqueness for pure- Neumann condtion 5. FDM for 2D steady state Heat equation 1. Global Error2. The 2-dimensional Steady-state Heat Eq.3. Singular perturbation and boundary layers4. Initial Value Problem for ODE  FDM for 2D steady state Heat equation 1. Global Error2. The 2-dimensional Steady-state Heat Eq.3. Singular perturbation and boundary layers4. Initial Value Problem for ODE 6. Advection Equation and ODE 1. Advection Equation and its solution2. Duhamels priciple3. Lipschitz Continuity4. Existence of solution of ODE 7. FDM for Ordinary Differential Equation(ODE) 1. One-step method2. Multistep method(LMN)3. Comparison between One-step and Multi step method4. Zero-Stability  FDM for Ordinary Differential Equation(ODE) 1. One-step method2. Multistep method(LMN)3. Comparison between One-step and Multi step method4. Zero-Stability 8. Stability for FDM 1. Zero-stability2. Absolute-stability 9. Absolute Stability and its region 1. Absolute statbility2. Stability region for linear multistep method3. Plotting Stability region4. Diffusion Equation and Parabolic equation.  Absolute Stability and its region 1. Absolute statbility2. Stability region for linear multistep method3. Plotting Stability region4. Diffusion Equation and Parabolic equation. 10. Stability and Convergency for diffusion equation. Stability analysis by eigen values 11. Diffusion Equation 1. Convergence2. Lax Equivalence Theorem3. Von Neumann analysis4. FDM for heat equation.13분 30초 까지 음성 없음.  Diffusion Equation 1. Convergence2. Lax Equivalence Theorem3. Von Neumann analysis4. FDM for heat equation. 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  FDM for advection equation. 1. Method of lines discretization(MOL)2. Lax-Friedrichs (LxF)3. Lax-Wendroff (LxW)4. Upwind 14. Von Neumann analysis for LxF, LxW, Upwind, etc 1. 폰노이만 분석2. Lax-Friedrichs3. Lax-Wendroff4. Upwind 15. FVM (1) 1. Conservation Law2. General formulation3. Numerical Flux  FVM (1) 1. Conservation Law2. General formulation3. Numerical Flux34분 이후로 음성 없음. 16. FVM (2) 1. CFL Condition2. Flux formulation 17. FVM (3) - Numerical Fluxes 1. Lax-Friedrichs2. Richmyer method3. Upwind method4. Godunovs method5. High - Resolution Mthods6. Limiters  FVM (3) - Numerical Fluxes 1. Lax-Friedrichs2. Richmyer method3. Upwind method4. Godunovs method5. High - Resolution Mthods6. Limiters 18. FVM (4) 1. Limiters2. TVD 19. FVM (5) - Limiters 1. Superbee limiter2. Flux Limiters3. Harten Theorem4. FVM in n-dimensional space  FVM (5) - Limiters 1. Superbee limiter2. Flux Limiters3. Harten Theorem4. FVM in n-dimensional space 20. FEM (Finite Element Mthod) (1) 1. Introduction2. Weak Derivatives3. Sobolev Spaces  FEM (Finite Element Mthod) (1) 1. Introduction2. Weak Derivatives3. Sobolev Spaces 21. FEM (2) 1. General spaces2. Approximations 22. FEM (3) 1. Weak forms2. Useful Theorems for FEM3. Greens formula  FEM (3) 1. Weak forms2. Useful Theorems for FEM3. Greens formula 23. FEM (4) 1. Formulation for FEM2. Reference triangle 24. FEM (5) Trace Thoerem, Sobolev Embedding  FEM (5) Trace Thoerem, Sobolev Embedding #### 연관 자료 #### 사용자 의견

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