수치 편미분 방정식

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수치 편미분 방정식

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페이스북 트위터 카카오톡 네이버밴드 링크복사

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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 equation 2. FDM for Steady state heat equation 3. FDM for various boundary condition.
	FDM for steady state Heat equation	1. Heat equation 2. FDM for Steady state heat equation 3. 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 Error 2. The 2-dimensional Steady-state Heat Eq. 3. Singular perturbation and boundary layers 4. Initial Value Problem for ODE
	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
6.	Advection Equation and ODE	1. Advection Equation and its solution 2. Duhamels priciple 3. Lipschitz Continuity 4. Existence of solution of ODE
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
	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
8.	Stability for FDM	1. Zero-stability 2. Absolute-stability
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.
	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.
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.
	Diffusion Equation	1. Convergence 2. Lax Equivalence Theorem 3. Von Neumann analysis 4. 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 분석 2. Lax-Friedrichs 3. Lax-Wendroff 4. Upwind
15.	FVM (1)	1. Conservation Law 2. General formulation 3. Numerical Flux
	FVM (1)	1. Conservation Law 2. General formulation 3. Numerical Flux 34분 이후로 음성 없음.
16.	FVM (2)	1. CFL Condition 2. Flux formulation
17.	FVM (3) - Numerical Fluxes	1. Lax-Friedrichs 2. Richmyer method 3. Upwind method 4. Godunovs method 5. High - Resolution Mthods 6. Limiters
	FVM (3) - Numerical Fluxes	1. Lax-Friedrichs 2. Richmyer method 3. Upwind method 4. Godunovs method 5. High - Resolution Mthods 6. Limiters
18.	FVM (4)	1. Limiters 2. TVD
19.	FVM (5) - Limiters	1. Superbee limiter 2. Flux Limiters 3. Harten Theorem 4. FVM in n-dimensional space
	FVM (5) - Limiters	1. Superbee limiter 2. Flux Limiters 3. Harten Theorem 4. FVM in n-dimensional space
20.	FEM (Finite Element Mthod) (1)	1. Introduction 2. Weak Derivatives 3. Sobolev Spaces
	FEM (Finite Element Mthod) (1)	1. Introduction 2. Weak Derivatives 3. Sobolev Spaces
21.	FEM (2)	1. General spaces 2. Approximations
22.	FEM (3)	1. Weak forms 2. Useful Theorems for FEM 3. Greens formula
	FEM (3)	1. Weak forms 2. Useful Theorems for FEM 3. Greens formula
23.	FEM (4)	1. Formulation for FEM 2. Reference triangle
24.	FEM (5)	Trace Thoerem, Sobolev Embedding
	FEM (5)	Trace Thoerem, Sobolev Embedding