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Numerical Modeling Lecture Notes
Welcome to the Numerical Modeling Lecture Notes
The finite difference method (FDM)
Algebraic approximation of the first derivative
Truncation Error
Estimates of the truncation error
Finite difference formulas for the 1st derivative
Evaluating the truncation error
The linear advection equation
The exact equation
The difference equation
Solution of the difference equation
Analysis of the solution of the difference equation
Stability of numerical schemes
Consistency, convergence and stability
Von Neumann Stability Analysis
Matrix Stability Analysis
Numerical schemes for the linear 1-d advection equation
The Leapfrog Scheme
The Upwind Scheme
The Lax-Wendroff Scheme
The MacCormack Scheme
The Crank-Nicholson Scheme
The Implicit Scheme
Total Variation Diminishing Schemes
The semi-lagrangian scheme
The two dimensional advection equation
Gravity Waves
Linear 1-d Gravity Waves
Solution on a regular grid
Solution on a staggered grid
Bibliography
repository
open issue
Index