Finite Difference Methods

Grid-based derivative approximations and time stepping techniques.

This section of The Numerics Lab is dedicated to Finite Difference Methods (FDM). We focus on the implementation of grid-based derivative approximations, advection and diffusion examples, stability analysis, CFL conditions, boundary conditions, and explicit vs implicit time stepping schemes.

Examples

1-D Linear Convection

Explicit upwind FDM for scalar transport. Introduces numerical diffusion and the CFL condition.

Starting Points & Planned Topics

  • Linear advection (upwind vs central differencing)
  • 1D diffusion equation
  • Poisson equation solvers
  • Stability and CFL experiments
View directory on GitHub
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