Welcome to the Numerical Modeling Lecture Notes

These are the lecture notes for the GEOF211 course on Numerical Modeling, Spring Semester 2023. Course information can be found at course page.

• 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
• Bibliography