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...

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

(PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. In this method, functions are represented...

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

operator-based wave equation often as a relativistic wave equation. The wave equation is a hyperbolic partial differential equation describing waves, including...

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

The shallow-water equations (SWE) are a set of hyperbolic partial differential equations (or parabolic if viscous shear is considered) that describe the...

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

also be found for hyperbolic and parabolic partial differential equation. The method is to reduce a partial differential equation (PDE) to a family of...

of the hydrological cycle. The advection equation is a first-order hyperbolic partial differential equation that governs the motion of a conserved scalar...

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

mathematics and physics, the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier...

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

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

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

Friedrichs, is a numerical method for the solution of hyperbolic partial differential equations based on finite differences. The method can be described...

the EFE are a system of ten coupled, nonlinear, hyperbolic-elliptic partial differential equations. The above form of the EFE is the standard established...

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

ellipses and hyperbolas. Hyperbolic growth Hyperbolic partial differential equation Hyperbolic sector Hyperboloid structure Hyperbolic trajectory Hyperboloid...

the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. This...

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

In mathematics, the Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow...

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

class of numerical discretization methods for solving hyperbolic partial differential equations. In the so-called upwind schemes typically, the so-called...

and specifically partial differential equations (PDEs), d´Alembert's formula is the general solution to the one-dimensional wave equation: u t t − c 2 u...

switching from a parabolic (dissipative) to a hyperbolic (includes a conservative term) partial differential equation, there is the possibility of phenomena...

In fluid dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard...

property of certain discretization schemes used to solve hyperbolic partial differential equations. The most notable application of this method is in computational...