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

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

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

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

In mathematics a partial differential algebraic equation (PDAE) set is an incomplete system of partial differential equations that is closed with a set...

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

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

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

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

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

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

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

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

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

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

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

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...

Einstein tensor allows the EFE to be written as a set of nonlinear partial differential equations when used in this way. The solutions of the EFE are the components...

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

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

mathematical analysis of partial differential equations uses analytical techniques to study partial differential equations. The subject has connections...

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

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 stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless...

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

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

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...