Numerical Models for Differential Problems by Alfio Quarteroni

Author:Alfio Quarteroni
Language: eng
Format: epub, pdf
Publisher: Springer Milan, Milano

1 13.1 A scalar transport problem

Let us consider the following scalar hyperbolic problem

(13.1)

where a ∈ ℝ \ {0}. The solution of such problem is a wave travelling at velocity a, given by

We consider the curves x(t) in the plane (x,t), solutions of the following ordinary differential equation

for varying values of x 0 ∈ ℝ.

Such curves are called characteristic lines (often simply characteristics) and the solution along these lines remains constant, for

In the case of the more general problem

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