In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function...

A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent...

In mathematics, a hyperbolic partial differential equation of order n {\displaystyle n} is a partial differential equation (PDE) that, roughly speaking...

Second-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second-order linear PDE in two...

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions...

In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different...

In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its...

methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs)...

Such an equation is an ordinary differential equation (ODE). A linear differential equation may also be a linear partial differential equation (PDE), if...

Stochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary...

with partial differential equations which may be with respect to more than one independent variable. A linear differential equation is a differential equation...

A separable partial differential equation can be broken into a set of equations of lower dimensionality (fewer independent variables) by a method of separation...

methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be...

mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions...

Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas...

mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in...

In mathematics, a first-order partial differential equation is a partial differential equation that involves only first derivatives of the unknown function...

the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the linear partial differential equation: ∇ 2 f = − k 2...

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution...

(real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function...

classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of...

mathematical finance, the Black–Scholes equation, also called the Black–Scholes–Merton equation, is a partial differential equation (PDE) governing the price evolution...

mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability...

The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium...

See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations....

Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form...

Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the...

In mathematics, a dispersive partial differential equation or dispersive PDE is a partial differential equation that is dispersive. In this context, dispersion...

The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves...

of partial differential equation topics. Partial differential equation Nonlinear partial differential equation list of nonlinear partial differential equations...