Editing Euler equations (fluid dynamics) (section)

===Spatial dimensions===
For certain problems, especially when used to analyze compressible flow in a duct or in case the flow is cylindrically or spherically symmetric, the one-dimensional Euler equations are a useful first approximation. Generally, the Euler equations are solved by [[Riemann]]'s [[method of characteristics]]. This involves finding curves in plane of independent variables (i.e., <math>x</math> and <math>t</math>) along which [[partial differential equation]]s (PDEs) degenerate into [[ordinary differential equation]]s (ODEs). [[Numerical analysis|Numerical solutions]] of the Euler equations rely heavily on the method of characteristics.