Midterm Outline
- Necessary and Sufficient Conditions for Convergence (Lax-Richtmyer Theorem)
- Stability
- Sufficient conditions for stability of FD methods for first order and second order PDEs.
- CFL Condition.
- Von Neumann Analysis.
- Accuracy Analysis
- Real-space approaches.
- Fourier-space approaches.
- First Order Hypobolic PDEs
- Method of Characteristics
- Lax-Wendroff FD Method
- Upwinding FD Method
- Second Order Hypobolic PDEs
- Central in Time and Central in Space FD Method
- Parabolic PDEs
- Representation of analytic solution in terms of Green's functions.
- Crank-Nicolson FD Method
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