- Background on PDE Theory
- § E.1: Examples and Classification
Including
- Elliptic, Parabolic, Hyperbolic
- Steady-state, Dynamic
- Linear, Non-linear
- Cannonical Problems
- § E.2: Derivation and Solutions
- § E.3: Fourier Analysis and Well-posedness
- Chapter 2: Two-point BVP (ODE)
- § 2.4: Simple Numerical Method
- § 2.5-2.11: Stability, Consistency, Convergence
- § 2.12: Neumann Boundary Conditions
- Existence, Uniqueness, Well-posedness
- Generalizations
- Chapter 3: Elliptic Equations
- § 3.2: 5-point Stencil
- § 3.4-3.5: Accuracy and Stability
- Chapter 4: Solution Methods for Resulting Linear Systems
- § 4.1-4.2: Jacobi, Gauss-Seidel and SOR
- § 4.3: Conjugate Gradients
- § 4.4: GMRES
- Chapter 9: Parabolic Equations
- Methods and Stencils
- § 9.1: Accuracy
- § 9.2-9.3: Stability
- § 9.4: Stiffness
- § 9.5: Convergence
- § 9.6: Von Neumann Stability Analysis
- Dissipation and Dispersion
- Generalizations
- Chapter 10: Hyperbolic Equations
- § 10.1: Advection
- § 10.2: Stability
- § 10.3: Higher Order Methods
- § 10.4: Upwind Methods
- § 10.5: Von Neumann Stability Analysis
- § 10.7: CFL Condition
- Dissipation and Dispersion
- Generalizations
- Wave Equation
- Finite Element Method
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