In mathematics, a hyperbolic partial differential equation of order n {\displaystyle n} is a partial differential equation (PDE) that, roughly speaking...
8 KB (1,241 words) - 13:53, 17 July 2025
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...
8 KB (1,149 words) - 01:57, 5 June 2025
In mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are...
18 KB (2,591 words) - 13:19, 22 July 2025
mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The...
49 KB (6,800 words) - 08:09, 10 June 2025
In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different...
9 KB (1,085 words) - 09:38, 1 March 2025
(PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. In this method, functions are represented...
17 KB (1,942 words) - 10:04, 18 July 2025
The telegrapher's equations (or telegraph equations) are a set of two coupled, linear partial differential equations that model voltage and current along...
34 KB (4,745 words) - 20:26, 2 July 2025
operator-based wave equation often as a relativistic wave equation. The wave equation is a hyperbolic partial differential equation describing waves, including...
60 KB (10,782 words) - 21:41, 4 June 2025
Method of characteristics (redirect from Charpit-Lagrange equations)
also be found for hyperbolic and parabolic partial differential equation. The method is to reduce a partial differential equation (PDE) to a family of...
18 KB (2,221 words) - 17:19, 12 June 2025
In mathematics, a first-order partial differential equation is a partial differential equation that involves the first derivatives of an unknown function...
14 KB (3,130 words) - 06:52, 10 October 2024
The shallow-water equations (SWE) are a set of hyperbolic partial differential equations (or parabolic if viscous shear is considered) that describe the...
37 KB (4,776 words) - 11:54, 3 June 2025
the EFE are a system of ten coupled, nonlinear, hyperbolic-elliptic partial differential equations. The above form of the EFE is the standard established...
35 KB (5,104 words) - 21:05, 17 July 2025
Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas...
17 KB (2,804 words) - 16:06, 13 June 2025
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium...
21 KB (3,102 words) - 17:14, 13 July 2025
specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier...
58 KB (9,878 words) - 11:03, 19 July 2025
Advection (redirect from Advection equation)
of the hydrological cycle. The advection equation is a first-order hyperbolic partial differential equation that governs the motion of a conserved scalar...
9 KB (1,079 words) - 06:26, 10 March 2025
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form...
76 KB (7,991 words) - 23:17, 26 June 2025
Hyperbola (redirect from Hyperbolic arc)
ellipses and hyperbolas. Hyperbolic growth Hyperbolic partial differential equation Hyperbolic sector Hyperboloid structure Hyperbolic trajectory Hyperboloid...
76 KB (13,603 words) - 04:25, 12 July 2025
An eikonal equation (from Greek εἰκών, image) is a non-linear first-order partial differential equation that is encountered in problems of wave propagation...
23 KB (3,770 words) - 01:49, 12 May 2025
Lax–Friedrichs method (category Numerical differential equations)
Friedrichs, is a numerical method for the solution of hyperbolic partial differential equations based on finite differences. The method can be described...
7 KB (1,194 words) - 03:23, 18 July 2025
Such an equation is an ordinary differential equation (ODE). A linear differential equation may also be a linear partial differential equation (PDE), if...
30 KB (4,754 words) - 18:32, 3 July 2025
In mathematics a partial differential algebraic equation (PDAE) set is an incomplete system of partial differential equations that is closed with a set...
3 KB (414 words) - 01:07, 7 December 2024
In mathematics, the Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow...
25 KB (3,209 words) - 16:05, 13 June 2025
the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. This...
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Initial condition (category Differential equations)
value of a recurrence relation, discrete dynamical system, hyperbolic partial differential equation, or even a seed value of a pseudorandom number generator...
8 KB (1,274 words) - 21:04, 12 July 2025
Differential Equations II: Qualitative Studies of Linear Equations, Springer-Verlag, ISBN 978-1-4419-7051-0 Taylor, Michael E. (1996b), Partial Differential Equations...
129 KB (17,641 words) - 09:51, 24 June 2025
the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the elliptic partial differential equation: ∇ 2 f = − k 2...
20 KB (2,975 words) - 18:26, 19 May 2025
Nonlinear system (redirect from Nonlinear differential equation)
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...
21 KB (2,645 words) - 12:32, 25 June 2025
In fluid dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard...
79 KB (13,150 words) - 19:33, 15 July 2025
D'Alembert's formula (redirect from D'alembert's solution to the wave equation)
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...
5 KB (1,075 words) - 07:05, 1 May 2025