Method of Characteristics

A technique for solving certain partial differential equations (notably first-order and some hyperbolic equations) by reducing the PDE to ordinary differential equations along curves called characteristics, along which the PDE becomes an ODE for the unknown and its derivatives.

A procedure for reducing certain partial differential equations—typically first-order or quasilinear hyperbolic equations—to ordinary differential equations by following characteristic curves along which the PDE becomes an ODE.

A technique for solving first-order partial differential equations by reducing them to ordinary differential equations along curves (characteristics) in the domain on which the PDE prescribes directional derivatives; solutions are constructed by integrating ODEs along these characteristic curves.