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Introduction of this course 1-1 | 1. Introduction of this course 2. Preliminaries |
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Introduction of this course 1-2 | ![]() |
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Introduction of this course 2 | 1. Introduction of this course 2. Preliminaries |
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Steady state and Boundary value problems 1 | 1. Heat Equation 2. Locla Trucation error, Global error 3. Dirichlet-Neumann Boundary condition |
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Steady state and Boundary value problems 2 | 1. Dirichlet-Neumann boundary condition 2. Neumann boundary conditon 3. 2D steady state heat equation |
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Steady state and Boundary value problem | 1. 2D steady state heat equation 2. Singular perturbation and boundary layer |
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The Initial Value Problem for Ordinary Differential Equations 1 | 1. Linear Ordinary Differential Equation 2. Lipschitz continuity |
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The Initial Value Problem for Ordinary Differential Equations | One-step method for ODE | ![]() |
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The Initial Value Problem for Ordinary Differential Equations | Multistep method for ODE | ![]() |
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Zero-Stability and Convergence for Initial value Problem | Stability of one-step method | ![]() |
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Absolute Stability for Ordinary Differential Equations | Absolute Stability of one-step and multistep methods, Stability Regions | ![]() |
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Diffusion Equations and Parabolic Problems | Discretization of Diffusion Equations | ![]() |
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Diffusion Equations and Parabolic Problems | Matrix form of Crank-Nicolson, LTE, Stability | ![]() |
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Diffusion Equations and Parabolic Problems | Stability of Crank-Nicolson and Forward Euler | ![]() |
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Diffusion Equations and Parabolic Problems | Stiffness of heat equations, Convergence | ![]() |
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Diffusion Equations and Parabolic Problems | Lax Equivalence Theorem, Von-Neumann Analysis | ![]() |
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Diffusion Equations and Parabolic Problems | Von-Neumann Analysis, Multidimensional Problems | ![]() |
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Advection Equations and Hyperbolic equations | Method of Lines Discretiztion(MOL) | ![]() |
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Advection Equations and Hyperbolic equations | Method of Lines Discretiztion, Von-Neumann Analysis for MOL | ![]() |
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Advection Equations and Hyperbolic equations | Von-Neumann Analysis, CFL condition | ![]() |
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Finite Volume Method | Conservation Law, General Formulation | ![]() |
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Finite Volume Method | Conservation Law, CFLcondition, Numerical Fluxes | ![]() |
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Finite Volume Method | Numerical Fluxes | ![]() |
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Finite Volume Method | Limiters | ![]() |
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Finite Volume Method | Limiters, TVD | ![]() |
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Finite Volume Method | FVM in n-dimensional space | ![]() |
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Finite Volume Method | FVM in n-dimensional space | ![]() |
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Finite Element Method | Sobolev Spaces | ![]() |
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Finite Element Method | Sobolev Spaces | ![]() |
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Finite Element Method | Sobolev Spaces | ![]() |
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Finite Element Method | FEM - Implementation | ![]() |
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Finite Element Method | FEM - Implementation | ![]() |
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Finite Element Method | FEM for 2D Poissong Equation, ProgrammingWeak solutions | ![]() |
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Finite Element Method | Existence and Uniqueness of weak solutions | ![]() |
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Finite Element Method | Dirichlet Problem, Neumann Problem | ![]() |
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Finite Element Method | Minimization Problem, Discrete Problem | ![]() |