1 Method of Characteristics
The method of characteristics is a technique for solving certain Partial Differential Equations. Typically, it applies to first-order equations though in general can be found for [[hyperbolic-partial-differential-equations]] and [[parabolic-partial-differential-equations]].
The method involves reducing a PDE to a family of ODEs along which the solution can be integrated from some initial data given on a suitable hypersurface.
1.1 Characteristics of First-Order PDEs
For a first-order PDE, the method of characteristics discovers characteristic curves along which the PDE becomes an ODE. Once found, these can be solved along the characteristic curves and transformed into a solution for the original PDE.