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...

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

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...

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

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

those functions. The term "ordinary" is used in contrast with partial differential equations (PDEs) which may be with respect to more than one independent...

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

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

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

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

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

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

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

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

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

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

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...

methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs...

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

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

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

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

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...

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

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

system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear...

The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian...