• 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
  • Thumbnail for Partial differential equation
    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
  • Thumbnail for Wave equation
    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
  • 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
  • Thumbnail for Shallow water equations
    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
  • Thumbnail for Burgers' equation
    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
  • Thumbnail for Heat equation
    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
  • Thumbnail for Maxwell's equations
    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
  • Thumbnail for Hyperbola
    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
  • Thumbnail for Korteweg–De Vries equation
    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...
    2 KB (110 words) - 07:45, 1 May 2024
  • 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
  • Thumbnail for Differential geometry of surfaces
    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
  • 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
  • Thumbnail for Euler equations (fluid dynamics)
    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
  • 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