Ordinary differential equation

Differential equations
Scope
Fields
Applied mathematics
Social sciences
List of named differential equations
Classification
Types
By variable type
Features
  • Notation
Relation to processes
  • 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

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions.[1] The term "ordinary" is used in contrast with partial differential equations (PDEs) which may be with respect to more than one independent variable,[2] and, less commonly, in contrast with stochastic differential equations (SDEs) where the progression is random.[3]

  1. ^ Dennis G. Zill (15 March 2012). A First Course in Differential Equations with Modeling Applications. Cengage Learning. ISBN 978-1-285-40110-2. Archived from the original on 17 January 2020. Retrieved 11 July 2019.
  2. ^ "What is the origin of the term "ordinary differential equations"?". hsm.stackexchange.com. Stack Exchange. Retrieved 2016-07-28.
  3. ^ Karras, Tero; Aittala, Miika; Aila, Timo; Laine, Samuli (2022). "Elucidating the Design Space of Diffusion-Based Generative Models". arXiv:2206.00364 [cs.CV].
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