Partial differential equation

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A partial differential equation is an equation involving a function of several independent variables and its partial derivatives. It describes how a quantity changes with respect to more than one coordinate, such as position and time.

Important examples include the wave equation, heat equation, Laplace equation, Schrödinger equation, Maxwell's equations, and the Navier–Stokes equations. These model propagation, diffusion, fields, fluids, and quantum systems.

Solutions are determined not only by the equation but also by boundary conditions and initial conditions. Different classifications, including elliptic, parabolic, and hyperbolic equations, reflect distinct mathematical behaviour.

Partial differential equations are central to physics, engineering, geometry, finance, biology, meteorology, and numerical simulation. Many require approximate computational methods rather than closed-form solutions.

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• Source / publisher: Wikipedia
• URL type: WWW
• Credits: Wikipedia
• URL: https://en.wikipedia.org/wiki/Partial_differential_equation