The (1+1)D Advection Equation

where is a real constant [176]. It is complemented by the initial condition

Here, the solution is assumed continuously differentiable (though it need not be

That is, the initial data travels to the left or right (depending on the sign of ) with speed . Despite its simplicity, it is often used as a model for numerical schemes [95].

Stefan Bilbao 2002-01-22