Meta tags:

Headings (most frequently used words):

boundary, dirichlet, condition, contents, examples, other, conditions, see, also, references, ode, pde, applications,

Text of the page (most frequently used words):
the (38), #boundary (29), dirichlet (15), #condition (14), edit (11), and (10), conditions (9), differential (9), wikipedia (7), finite (6), element (6), for (6), where (6), page (5), equations (5), engineering (5), fixed (5), theory (5), displaystyle (5), partial (5), contents (4), search (4), neumann (4), other (4), cauchy (4), form (4), function (4), equation (4), theorem (4), hide (4), move (4), sidebar (4), toggle (3), view (3), this (3), with (3), order (3), method (3), history (3), fluid (3), dynamics (3), robin (3), also (3), are (3), that (3), held (3), ordinary (3), examples (3), values (3), solution (3), solutions (3), sciences (3), type (3), existence (3), tools (3), main (3), languages (2), table (2), contact (2), about (2), privacy (2), policy (2), terms (2), may (2), non (2), was (2), short (2), description (2), wikidata (2), from (2), one (2), cheng (2), analysis (2), references (2), see (2), beam (2), example (2), applications (2), domain (2), take (2), known (2), defined (2), quad (2), laplace (2), operator (2), nabla (2), pde (2), ode (2), integral (2), dependent (2), essential (2), variable (2), mathematics (2), such (2), named (2), problem (2), crank (2), nicolson (2), picard (2), lindelöf (2), kutta (2), runge (2), kovalevskaya (2), liouville (2), sturm (2), green (2), euler (2), variables (2), galerkin (2), difference (2), exponential (2), special (2), asymptotic (2), series (2), general (2), stochastic (2), linear (2), appearance (2), upload (2), file (2), changes (2), links (2), read (2), article (2), log (2), create (2), account (2), donate (2), menu (2), add, topic, mobile, cookie, statement, statistics, developers, code, conduct, legal, safety, contacts, disclaimers, text, available, under, additional, apply, using, site, you, agree, registered, trademark, profit, organization, wikimedia, foundation, inc, use, creative, commons, attribution, sharealike, license, rendered, parsoid, last, edited, october, 2025, utc, hidden, categories, matches, articles, category, retrieved, https, org, index, php, title, dirichlet_boundary_condition, oldid, 1318601261, 2009, second, dimension, models, 3rd, boston, mcgraw, hill, 110, 978, 126761, isbn, introduction, reddy, 2005, heritage, early, 302, 1016, enganabound, 2004, 001, doi, 268, elements, many, possible, including, latter, combination, mixed, viscous, fluids, states, solid, will, have, zero, velocity, relative, slip, node, circuit, voltage, electrostatics, surface, temperature, heat, transfer, end, position, space, civil, mechanical, following, would, considered, denotes, forall, omega, instance, interval, given, numbers, alpha, beta, weighted, unknown, appearing, expression, termed, its, specification, constitutes, primary, same, weight, imposed, takes, along, question, finding, referred, after, 1805, 1859, peter, gustav, lejeune, first, courant, hrennikoff, jeffreys, lipschitz, boole, fourier, wroński, lagrange, clairaut, alembert, jacob, bernoulli, leibniz, newton, list, people, wkb, approximation, variation, parameters, undetermined, coefficients, separation, reduction, perturbation, transforms, integrating, factor, petrov, volume, infinite, response, formula, ansatz, characteristics, inspection, methods, dirac, delta, numerical, integration, functions, rate, convergence, stability, lyapunov, phase, portrait, floquet, abel, identity, wronskian, periodic, initial, topics, carathéodory, peano, well, posed, uniqueness, delay, discrete, analogue, relation, processes, notation, features, nonhomogeneous, homogeneous, exact, coupled, decoupled, autonomous, independent, fractional, integro, algebraic, types, classification, population, economics, social, dynamical, systems, chaos, continuum, mechanics, applied, geology, biology, chemistry, physics, astronomy, natural, fields, scope, constraint, free, encyclopedia, item, projects, printable, version, download, pdf, print, export, switch, legacy, parser, get, shortened, url, cite, information, permanent, link, related, what, here, actions, english, talk, українська, svenska, русский, română, português, polski, 한국어, 日本語, italiano, français, español, deutsch, català, bosanski, subsection, top, personal, pages, recent, community, portal, learn, help, contribute, random, current, events, navigation, jump, content,

Text of the page (random words):
dirichlet boundary condition wikipedia 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 examples toggle examples subsection 1 1 ode 1 2 pde 1 3 applications 2 other boundary conditions 3 see also 4 references toggle the table of contents dirichlet boundary condition 15 languages bosanski català deutsch español français italiano 日本語 한국어 polski português română русский svenska українська 中文 edit 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 type of constraint on solutions to differential equations 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 in mathematics the dirichlet boundary condition is imposed on an ordinary or partial differential equation such that the values that the solution takes along the boundary of the domain are fixed the question of finding solutions to such equations is known as the dirichlet problem in the sciences and engineering a dirichlet boundary condition may also be referred to as a fixed boundary condition or boundary condition of the first type it is named after peter gustav lejeune dirichlet 1805 1859 1 in finite element analysis the essential or dirichlet boundary condition is defined by weighted integral form of a differential equation 2 the dependent unknown u in the same form as the weight function w appearing in the boundary expression is termed a primary variable and its specification constitutes the essential or dirichlet boundary condition examples edit ode edit for an ordinary differential equation for instance y y 0 displaystyle y y 0 the dirichlet boundary conditions on the interval a b take the form y a α y b β displaystyle y a alpha quad y b beta where α and β are given numbers pde edit for a partial differential equation for example 2 y y 0 displaystyle nabla 2 y y 0 where 2 displaystyle nabla 2 denotes the laplace operator the dirichlet boundary conditions on a domain ω r n take the form y x f x x ω displaystyle y x f x quad forall x in partial omega where f is a known function defined on the boundary ω applications edit for example the following would be considered dirichlet boundary conditions in mechanical engineering and civil engineering beam theory where one end of a beam is held at a fixed position in space in heat transfer where a surface is held at a fixed temperature in electrostatics where a node of a circuit is held at a fixed voltage in fluid dynamics the no slip condition for viscous fluids states that at a solid boundary the fluid will have zero velocity relative to the boundary other boundary conditions edit many other boundary conditions are possible including the cauchy boundary condition and the mixed boundary condition the latter is a combination of the dirichlet and neumann conditions see also edit neumann boundary condition robin boundary condition boundary conditions in fluid dynamics references edit cheng a cheng d t 2005 heritage and early history of the boundary element method engineering analysis with boundary elements 29 3 268 302 doi 10 1016 j enganabound 2004 12 001 reddy j n 2009 second order differential equations in one dimension finite element models an introduction to the finite element method 3rd ed boston mcgraw hill p 110 isbn 978 0 07 126761 8 retrieved from https en wikipedia org w index php title dirichlet_boundary_condition oldid 1318601261 category boundary conditions hidden categories articles with short description short description matches wikidata this page was last edited on 24 october 2025 at 21 27 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia legal safety contacts code of conduct developers statistics cookie statement mobile view search search toggle the table of contents dirichlet boundary condition 15 languages add topic