## 주메뉴

### 수치편미분방정식

• 연세대학교
• 이은정 • 주제분류
자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
• 강의학기
2011년 1학기
• 조회수
12,848
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This course focuses on the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic, and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics includes : Mathematical formulations; Finite difference method, Finite volume method, Collocation method, Finite element method
Introduction of this course 1-1 #### 차시별 강의      1 Introduction of this course 1-1 1. Introduction of this course2. Preliminaries 2 Introduction of this course 1-2 3 Introduction of this course 2 1. Introduction of this course2. Preliminaries 4 Steady state and Boundary value problems 1 1. Heat Equation2. Locla Trucation error, Global error3. Dirichlet-Neumann Boundary condition 5 Steady state and Boundary value problems 2 1. Dirichlet-Neumann boundary condition2. Neumann boundary conditon3. 2D steady state heat equation 6 Steady state and Boundary value problem 1. 2D steady state heat equation2. Singular perturbation and boundary layer 7 The Initial Value Problem for Ordinary Differential Equations 1 1. Linear Ordinary Differential Equation2. Lipschitz continuity 8 The Initial Value Problem for Ordinary Differential Equations One-step method for ODE 9 The Initial Value Problem for Ordinary Differential Equations Multistep method for ODE 10 Zero-Stability and Convergence for Initial value Problem Stability of one-step method 11 Absolute Stability for Ordinary Differential Equations Absolute Stability of one-step and multistep methods, Stability Regions 12 Diffusion Equations and Parabolic Problems Discretization of Diffusion Equations 13 Diffusion Equations and Parabolic Problems Matrix form of Crank-Nicolson, LTE, Stability 14 Diffusion Equations and Parabolic Problems Stability of Crank-Nicolson and Forward Euler 15 Diffusion Equations and Parabolic Problems Stiffness of heat equations, Convergence 16 Diffusion Equations and Parabolic Problems Lax Equivalence Theorem, Von-Neumann Analysis 17 Diffusion Equations and Parabolic Problems Von-Neumann Analysis, Multidimensional Problems 18 Advection Equations and Hyperbolic equations Method of Lines Discretiztion(MOL) 19 Advection Equations and Hyperbolic equations Method of Lines Discretiztion, Von-Neumann Analysis for MOL 20 Advection Equations and Hyperbolic equations Von-Neumann Analysis, CFL condition 21 Finite Volume Method Conservation Law, General Formulation 22 Finite Volume Method Conservation Law, CFLcondition, Numerical Fluxes 23 Finite Volume Method Numerical Fluxes 24 Finite Volume Method Limiters 25 Finite Volume Method Limiters, TVD 26 Finite Volume Method FVM in n-dimensional space 27 Finite Volume Method FVM in n-dimensional space 28 Finite Element Method Sobolev Spaces 29 Finite Element Method Sobolev Spaces 30 Finite Element Method Sobolev Spaces 31 Finite Element Method FEM - Implementation 32 Finite Element Method FEM - Implementation 33 Finite Element Method FEM for 2D Poissong Equation, ProgrammingWeak solutions 34 Finite Element Method Existence and Uniqueness of weak solutions 35 Finite Element Method Dirichlet Problem, Neumann Problem 36 Finite Element Method Minimization Problem, Discrete Problem #### 연관 자료 #### 사용자 의견

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