Visualization of heat transfer in a pump casing, created by solving the heat equation. Heat is being generated internally in the casing and being cooled at the boundary, providing a steady state temperature distribution.
Differential equations
Scope
Fields
Natural sciences
Engineering
Astronomy
Physics
Chemistry
Biology
Geology
Applied mathematics
Continuum mechanics
Chaos theory
Dynamical systems
Social sciences
Economics
Population dynamics
List of named differential equations
Classification
Types
Ordinary
Partial
Differential-algebraic
Integro-differential
Fractional
Linear
Non-linear
By variable type
Dependent and independent variables
Autonomous
Coupled / Decoupled
Exact
Homogeneous / Nonhomogeneous
Features
Order
Operator
Notation
Relation to processes
Difference (discrete analogue)
Stochastic
Stochastic partial
Delay
Solution
Existence and uniqueness
Picard–Lindelöf theorem
Peano existence theorem
Carathéodory's existence theorem
Cauchy–Kowalevski theorem
General topics
Initial conditions
Boundary values
Dirichlet
Neumann
Robin
Cauchy problem
Wronskian
Phase portrait
Lyapunov / Asymptotic / Exponential stability
Rate of convergence
Series / Integral solutions
Numerical integration
Dirac delta function
Solution methods
Inspection
Method of characteristics
Euler
Exponential response formula
Finite difference (Crank–Nicolson)
Finite element
Infinite element
Finite volume
Galerkin
Petrov–Galerkin
Green's function
Integrating factor
Integral transforms
Perturbation theory
Runge–Kutta
Separation of variables
Undetermined coefficients
Variation of parameters
People
List
Isaac Newton
Gottfried Leibniz
Jacob Bernoulli
Leonhard Euler
Joseph-Louis Lagrange
Józef Maria Hoene-Wroński
Joseph Fourier
Augustin-Louis Cauchy
George Green
Carl David Tolmé Runge
Martin Kutta
Rudolf Lipschitz
Ernst Lindelöf
Émile Picard
Phyllis Nicolson
John Crank
v
t
e
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.[1] In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
The study of differential equations consists mainly of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are soluble by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.
Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.
^Dennis G. Zill (15 March 2012). A First Course in Differential Equations with Modeling Applications. Cengage Learning. ISBN 978-1-285-40110-2.
and 25 Related for: Differential equation information
In mathematics, a differentialequation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions...
In mathematics, a partial differentialequation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function...
In mathematics, an ordinary differentialequation (ODE) is a differentialequation (DE) dependent on only a single independent variable. As with other...
In mathematics, a linear differentialequation is a differentialequation that is defined by a linear polynomial in the unknown function and its derivatives...
A stochastic differentialequation (SDE) is a differentialequation in which one or more of the terms is a stochastic process, resulting in a solution...
A differentialequation can be homogeneous in either of two respects. A first order differentialequation is said to be homogeneous if it may be written...
In mathematics, an ordinary differentialequation is called a Bernoulli differentialequation if it is of the form y ′ + P ( x ) y = Q ( x ) y n , {\displaystyle...
system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differentialequations) appear...
for ordinary differentialequations are methods used to find numerical approximations to the solutions of ordinary differentialequations (ODEs). Their...
In mathematics, delay differentialequations (DDEs) are a type of differentialequation in which the derivative of the unknown function at a certain time...
A differentialequation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and...
Second-order linear partial differentialequations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second-order linear PDE in two...
mathematics, a hyperbolic partial differentialequation of order n {\displaystyle n} is a partial differentialequation (PDE) that, roughly speaking, has...
A parabolic partial differentialequation is a type of partial differentialequation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent...
Fuzzy differentialequation are general concept of ordinary differentialequation in mathematics defined as differential inclusion for non-uniform upper...
dynamical system and differentialequation topics, by Wikipedia page. See also list of partial differentialequation topics, list of equations. Deterministic...
mathematics and physics, the heat equation is a certain partial differentialequation. Solutions of the heat equation are sometimes known as caloric functions...
mathematics. Fractional differentialequations, also known as extraordinary differentialequations, are a generalization of differentialequations through the application...
In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differentialequation that is quadratic in the unknown function...
for partial differentialequations is the branch of numerical analysis that studies the numerical solution of partial differentialequations (PDEs). In...
In mathematics, a system of differentialequations is a finite set of differentialequations. Such a system can be either linear or non-linear. Also, such...
Stochastic partial differentialequations (SPDEs) generalize partial differentialequations via random force terms and coefficients, in the same way ordinary...
Global Information