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

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, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are...

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

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

mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The...

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

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

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

In mathematical analysis, Clairaut's equation (or the Clairaut equation) is a differential equation of the form y ( x ) = x d y d x + f ( d y d x ) {\displaystyle...

a technique for solving particular partial differential equations. Typically, it applies to first-order equations, though in general characteristic curves...

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

A one-way wave equation is a first-order partial differential equation describing one wave traveling in a direction defined by the vector wave velocity...

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

A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written...

The telegrapher's equations (or telegraph equations) are a set of two coupled, linear partial differential equations that model voltage and current along...

Hamilton–Jacobi–Bellman equation from dynamic programming. The Hamilton–Jacobi equation is a first-order, non-linear partial differential equation − ∂ S ∂ t = H...

partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved. A first-order...

An eikonal equation (from Greek εἰκών, image) is a non-linear first-order partial differential equation that is encountered in problems of wave propagation...

The McKendrick–von Foerster equation is a linear first-order partial differential equation encountered in several areas of mathematical biology – for example...

a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or...

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...

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

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

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

equation First-order differential operator First-order linear differential equation First-order non-singular perturbation theory First-order partial differential...

systems. A Bäcklund transform is typically a system of first order partial differential equations relating two functions, and often depending on an additional...

vector of first order differential equations λ ˙ T ( t ) = − ∂ H ∂ x {\displaystyle {\dot {\lambda }}^{\mathsf {T}}(t)=-{\frac {\partial H}{\partial x}}} where...

The Navier–Stokes equations (/nævˈjeɪ stoʊks/ nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances...

thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier...