Midterm Outline

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

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