Editing Differential equation (section)

===Partial differential equations===
{{main|Partial differential equation}}
A [[partial differential equation]] (''PDE'') is a differential equation that contains unknown [[Multivariable calculus|multivariable function]]s and their [[partial derivatives]]. (This is in contrast to [[ordinary differential equations]], which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved in closed form, or used to create a relevant [[computer model]].

PDEs can be used to describe a wide variety of phenomena in nature such as [[sound]], [[heat]], [[electrostatics]], [[electrodynamics]], [[fluid flow]], [[Elasticity (physics)|elasticity]], or [[quantum mechanics]]. These seemingly distinct physical phenomena can be formalized similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional [[dynamical systems]], partial differential equations often model [[multidimensional systems]]. [[Stochastic partial differential equations]] generalize partial differential equations for modeling [[randomness]].