Numerical schemes for the linear 1-d advection equation

In this chapter we shall study several numerical schemes applied to the linear advection equation. The purpose of the study is to illustrate the concepts learned so far about the analysis of numerical scheme, as we apply them to solve a simple model of the advection process.

• 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