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edia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 mathematics toggle mathematics subsection 1 1 algebraic geometry 1 2 complex analysis 1 3 differential geometry 1 4 dynamical systems and chaos theory 1 5 mathematical physics 1 6 ordinary differential equations odes 1 7 riemannian geometry 2 physics toggle physics subsection 2 1 astrophysics 2 2 classical mechanics 2 3 electromagnetism 2 4 fluid dynamics and hydrology 2 5 general relativity 2 6 materials science 2 7 nuclear physics 2 8 plasma physics 2 9 quantum mechanics and quantum field theory 2 10 thermodynamics and statistical mechanics 2 11 waves mechanical or electromagnetic 3 engineering toggle engineering subsection 3 1 electrical and electronic engineering 3 2 game theory 3 3 mechanical engineering 3 4 nuclear engineering 3 5 optimal control 3 6 orbital mechanics 3 7 signal processing 3 8 transportation engineering 4 chemistry 5 biology and medicine toggle biology and medicine subsection 5 1 population dynamics 6 economics and finance 7 linguistics 8 military strategy 9 references toggle the table of contents list of named differential equations add languages add links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia 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 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 well posed problem picard lindelöf theorem peano existence theorem carathéodory s existence theorem cauchy kovalevskaya theorem general topics initial values boundary values dirichlet neumann robin cauchy periodic wronskian abel s identity sturm liouville theory floquet theory phase portrait stability lyapunov asymptotic exponential series solutions rate of convergence asymptotic series special functions numerical integration dirac delta function solution methods inspection method of characteristics ansatz 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 reduction of order runge kutta separation of variables undetermined coefficients variation of parameters wkb approximation people list newton leibniz jacob bernoulli d alembert clairaut euler lagrange laplace wroński fourier cauchy green dirichlet sturm liouville neumann robin boole kovalevskaya runge kutta lipschitz lindelöf picard jeffreys nicolson crank hrennikoff courant named equations v t e differential equations play a prominent role in many scientific areas mathematics physics engineering chemistry biology medicine economics etc this list presents differential equations that have received specific names area by area mathematics edit ablowitz kaup newell segur akns system clairaut s equation hypergeometric differential equation jimbo miwa ueno isomonodromy equations painlevé equations picard fuchs equation to describe the periods of elliptic curves schlesinger s equations sine gordon equation sturm liouville theory of orthogonal polynomials and separable partial differential equations universal differential equation algebraic geometry edit calabi flow in the study of calabi yau manifolds complex analysis edit cauchy riemann equations differential geometry edit equations for a minimal surface liouville s equation ricci flow used to prove the poincaré conjecture tzitzeica equation dynamical systems and chaos theory edit lorenz equations rabinovich fabrikant equations mathematical physics edit general legendre equation heat equation ishimori equation an integrable nonlinear spin field equation in 2 1 dimensions laplace s equation in potential theory poisson s equation in potential theory ordinary differential equations odes edit bernoulli differential equation cauchy euler equation riccati equation hill differential equation riemannian geometry edit gauss codazzi equations physics edit astrophysics edit chandrasekhar s white dwarf equation lane emden equation emden chandrasekhar equation hénon heiles system classical mechanics edit equation of motion euler s rotation equations in rigid body dynamics euler lagrange equation beltrami identity hamilton s equations hamilton jacobi equation lorenz equations in chaos theory n body problem in celestial mechanics wave action in continuum mechanics electromagnetism edit bloch equations continuity equation for conservation laws maxwell s equations poynting s theorem fluid dynamics and hydrology edit acoustic theory benjamin bona mahony equation biharmonic equation blasius boundary layer boussinesq approximation buoyancy boussinesq approximation water waves buckley leverett equation camassa holm equation chaplygin s equation continuity equation for conservation laws convection diffusion equation double diffusive convection davey stewartson equation euler tricomi equation falkner skan boundary layer gardner equation in hydrodynamics general equation of heat transfer geophysical fluid dynamics potential vorticity quasi geostrophic equations shallow water equations taylor goldstein equation groundwater flow equation richards equation hicks equation kadomtsev petviashvili equation in nonlinear wave motion kdv equation magnetohydrodynamics grad shafranov equation navier stokes equations euler equations burgers equation nonlinear schrödinger equation in water waves omega equation orr sommerfeld equation porous medium equation potential flow rayleigh bénard convection rayleigh plesset equation reynolds averaged navier stokes rans equations reynolds equation reynolds transport theorem riemann problem taylor von neumann sedov blast wave turbulence modeling turbulence kinetic energy tke k epsilon turbulence model k omega turbulence model spalart allmaras turbulence model vorticity equation whitham equation zebiak cane model 1 for el niño southern oscillation zeldovich taylor flow general relativity edit einstein field equations friedmann equations geodesic equation mathisson papapetrou dixon equations schrödinger newton equation materials science edit ginzburg landau equations in superconductivity london equations in superconductivity poisson boltzmann equation in molecular dynamics nuclear physics edit radioactive decay equations plasma physics edit gardner equation hasegawa mima equation kdv equation kuramoto sivashinsky equation parker transport equation vlasov equation quantum mechanics and quantum field theory edit dirac equation the relativistic wave equation for electrons and positrons gardner equation klein gordon equation knizhnik zamolodchikov equations in quantum field theory nonlinear schrödinger equation in quantum mechanics schrödinger equation 2 schwinger dyson equation yang mills equations in gauge theory thermodynamics and statistical mechanics edit boltzmann equation continuity equation for conservation laws diffusion equation heat equation kardar parisi zhang equation kuramoto sivashinsky equation liñán s equation as a model of diffusion flame maxwell relations zeldovich frank kamenetskii equation to model flame propagation waves mechanical or electromagnetic edit d alembert s wave equation eikonal equation in wave propagation euler poisson darboux equation in wave theory helmholtz equation engineering edit electrical and electronic engineering edit chua s circuit liénard equation to model oscillating circuits nonlinear schrödinger equation in fiber optics telegrapher s equations van der pol oscillator game theory edit differential game equations mechanical engineering edit euler bernoulli beam theory timoshenko beam theory nuclear engineering edit neutron diffusion equation 3 optimal control edit linear quadratic regulator matrix differential equation pde constrained optimization 4 5 riccati equation shape optimization orbital mechanics edit clohessy wiltshire equations planar reentry equations signal processing edit filtering theory kushner equation zakai equation rudin osher fatemi equation 6 in total variation denoising transportation engineering edit law of conservation in the kinematic wave model of traffic flow theory chemistry edit allen cahn equation in phase separation cahn hilliard equation in phase separation chemical reaction model brusselator oregonator master equation rate equation streeter phelps equation in water quality modeling biology and medicine edit allee effect in population ecology bidomain model in cardiology chemotaxis 7 in wound healing compartmental models in epidemiology sir model sis model hagen poiseuille equation in blood flow hodgkin huxley model in neural action potentials kardar parisi zhang equation for bacteria surface growth models kermack mckendrick theory in infectious disease epidemiology kuramoto model in biological and chemical oscillations mackey glass equations mckendrick von foerster equation in age structure modeling nernst planck equation in ion flux across biological membranes price equation in evolutionary biology reaction diffusion equation in theoretical biology fisher kpp equation in nonlinear traveling waves fitzhugh nagumo model in neural activation swift hohenberg equation in pattern formation replicator dynamics in theoretical biology verhulst equation in biological population growth von bertalanffy model in biological individual growth wilson cowan model in computational neuroscience population dynamics edit arditi ginzburg equations to describe predator prey dynamics kolmogorov petrovsky piskunov equation also known as fisher s equation to model population growth logistic differential equation for population growth generalized logistic differential equation for growth modeling lotka volterra equations to describe the dynamics of biological systems in which two species interact economics and finance edit bass diffusion model black scholes equation economic growth solow swan model k t s k t α δ k t textstyle k t s k t alpha delta k t ramsey cass koopmans model dynamic stochastic general equilibrium 8 feynman kac formula black scholes equation affine term structure modeling 9 fokker planck equation dupire equation local volatility hamilton jacobi bellman equation merton s portfolio problem optimal stopping malthusian growth model mean field game theory 10 optimal rotation age sovereign debt accumulation d r d g t t t textstyle dot d rd g t t t stochastic differential equation geometric brownian motion ornstein uhlenbeck process cox ingersoll ross model vidale wolfe advertising model linguistics edit replicator dynamics in evolutionary linguistics military strategy edit lanchester s laws in combat modeling references edit zebiak stephen e cane mark a 1987 a model el niño southern oscillation monthly weather review 115 10 2262 2278 doi 10 1175 1520 0493 1987 115 2262 ameno 2 0 co 2 issn 1520 0493 griffiths david j 2004 introduction to quantum mechanics 2nd ed prentice hall pp 1 2 isbn 0 13 111892 7 ragheb m 2017 neutron diffusion theory pdf choi youngsoo 2011 pde constrained optimization and beyond pdf heinkenschloss matthias 2008 pde constrained optimization pdf siam conference on optimization rudin leonid i osher stanley fatemi emad 1992 nonlinear total variation based noise removal algorithms physica d 60 1 4 259 268 bibcode 1992phyd 60 259r citeseerx 10 1 1 117 1675 doi 10 1016 0167 2789 92 90242 f cite journal cite uses deprecated parameter citeseerx help murray james d 2002 mathematical biology i an introduction pdf interdisciplinary applied mathematics vol 17 3rd ed new york springer pp 395 417 doi 10 1007 b98868 isbn 978 0 387 95223 9 fernández villaverde jesús 2010 the econometrics of dsge models pdf series 1 1 2 3 49 doi 10 1007 s13209 009 0014 7 s2cid 8631466 piazzesi monika 2010 affine term structure models pdf cardaliaguet pierre 2013 notes on mean field games from p l lions lectures at collège de france pdf v t e differential equations classification operations differential operator notation for differentiation ordinary partial differential algebraic integro differential fractional linear non linear holonomic attributes of variables dependent and independent variables homogeneous nonhomogeneous coupled decoupled order degree autonomous exact differential equation on jet bundles relation to processes difference discrete analogue stochastic stochastic partial delay solutions existence uniqueness picard lindelöf theorem peano existence theorem carathéodory s existence theorem cauchy kowalevski theorem solution topics wronskian phase portrait phase space lyapunov stability asymptotic stability exponential stability rate of convergence series solutions integral solutions numerical integration dirac delta function solution methods inspection substitution separation of variables method of undetermined coefficients variation of parameters integrating factor integral transforms euler method finite difference method crank nicolson method runge kutta methods finite element method finite volume method galerkin method perturbation theory examples list of named differential equations list of linear ordinary differential equations list of nonlinear ordinary differential equations list of nonlinear partial differential equations mathematicians isaac newton gottfried wilhelm leibniz leonhard euler jacob bernoulli émile picard józef maria hoene wroński ernst lindelöf rudolf lipschitz joseph louis lagrange augustin louis cauchy john crank phyllis nicolson carl david tolmé runge martin kutta sofya kovalevskaya retrieved from https en wikipedia org w index php title list_of_named_differential_equations oldid 1352594530 categories differential equations lists of equations hidden categories articles with short description short description is different from wikidata cs1 errors deprecated parameters this page was last edited on 5 may 2026 at 03 30 utc page was rendered with parsoid text is available under the 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