Analysis of Numerical Methods II

Polynomial Interpolation and Error Formulas Richardson Extrapolation Numerical Quadrature Numerical Differentiation and Finite Difference Operators Local Truncation Error and Global Error Consistency, Stability, and Convergence Finite Difference Boundary Value Problems Discrete Maximum Principles Elliptic and Poisson Equation Schemes Heat and Diffusion Equation Schemes Variable-Coefficient Diffusion Problems Implicit Time-Stepping Methods Forward Euler and First-Order Convergence Linear Multistep Methods Zero-Stability and Root Conditions Absolute Stability and A-Stability Runge-Kutta Methods and Butcher Tableaux Stiff ODEs and Time-Step Restrictions Von Neumann Stability Analysis Semi-Lagrangian Methods and Exponential Integrators