Difference between revisions of "Template:Differential equations"
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imported>Maschen (slight removal of redundancy) |
imported>Chongkian (match article name) |
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− | {{ | + | <includeonly>{{Sidebar with collapsible lists |
− | | | + | | name = Differential equations |
− | | | + | | bodyclass = plainlist |
− | | title | + | | titleclass = navbox-title |
− | + | | titlestyle = display:block;margin-bottom:0.2em; | |
− | | image | + | | title = [[Differential equation]]s |
+ | | image = [[File:Navier_Stokes_Laminar.svg|235px|Navier–Stokes differential equations used to simulate airflow around an obstruction]] | ||
+ | | captionstyle = padding-bottom:0.25em; | ||
+ | | caption = [[Navier–Stokes equations|Navier–Stokes differential equations]] used to simulate airflow around an obstruction. | ||
+ | | headingclass = navbox-abovebelow | ||
+ | | headingstyle = font-size:105%;display:block;margin-bottom:0.4em; | ||
+ | | listtitlestyle = text-align:center;padding-bottom:0; | ||
+ | | liststyle = padding-top:0; | ||
+ | | expanded = {{{expanded|{{{selected|{{{1|{{{cTopic|}}}}}}}}}}}} | ||
− | |||
− | |||
− | |||
− | |||
− | |||
+ | <!----------------------------- Scope -------------------------------> | ||
+ | | list1name = scope | ||
+ | | list1title = <div class="navbox-abovebelow" style="font-size:105%;padding:0;padding-bottom:0.1em;">Scope</div> | ||
+ | | list1 = | ||
+ | {{Sidebar |bodystyle={{subsidebar bodystyle}} |navbar=off | ||
+ | |headingstyle=padding-bottom:0; | ||
+ | |contentclass=hlist |contentstyle=padding-bottom:0.6em; | ||
+ | | heading1 = {{hlist|[[Natural science]]s|[[Engineering]]}} | ||
+ | | content1 = | ||
* [[Astronomy]] | * [[Astronomy]] | ||
* [[Physics]] | * [[Physics]] | ||
* [[Chemistry]] | * [[Chemistry]] | ||
− | * [[Biology]] | + | * <br/>[[Biology]] |
* [[Geology]] | * [[Geology]] | ||
− | + | | heading2 = [[Applied mathematics]] | |
− | + | | content2 = | |
* [[Continuum mechanics]] | * [[Continuum mechanics]] | ||
* [[Chaos theory]] | * [[Chaos theory]] | ||
* [[Dynamical systems]] | * [[Dynamical systems]] | ||
− | + | | heading3 = [[Social science]]s | |
− | + | | content3 = | |
* [[Economics]] | * [[Economics]] | ||
* [[Population dynamics]] | * [[Population dynamics]] | ||
+ | |content3style=padding-bottom:0; | ||
+ | }} | ||
+ | |||
+ | <!------------------------ Classification ---------------------------> | ||
+ | | heading2style = display:block;margin-top:0.1em; | ||
| heading2 = Classification | | heading2 = Classification | ||
− | | list3name | + | | list3name = types |
− | | list3title = | + | | list3title = Types |
− | | list3 | + | | list3 = |
− | + | {{Sidebar |bodystyle={{subsidebar bodystyle}} |navbar=off | |
− | + | | content1 = {{startflatlist}} | |
* [[Ordinary differential equation|Ordinary]] | * [[Ordinary differential equation|Ordinary]] | ||
* [[Partial differential equation|Partial]] | * [[Partial differential equation|Partial]] | ||
− | * [[ | + | * [[Differential-algebraic system of equations|Differential-algebraic]] |
* [[Integro-differential equation|Integro-differential]] | * [[Integro-differential equation|Integro-differential]] | ||
* [[Fractional differential equations|Fractional]] | * [[Fractional differential equations|Fractional]] | ||
* [[Linear differential equation|Linear]] | * [[Linear differential equation|Linear]] | ||
* [[Non-linear differential equation|Non-linear]] | * [[Non-linear differential equation|Non-linear]] | ||
− | + | {{endflatlist}} | |
− | | | + | | heading2 = By variable type |
− | | | + | | content2 = |
− | |||
* [[Dependent and independent variables]] | * [[Dependent and independent variables]] | ||
− | + | {{startflatlist}} | |
− | |||
− | |||
− | |||
− | |||
− | |||
* [[Autonomous differential equation|Autonomous]] | * [[Autonomous differential equation|Autonomous]] | ||
− | * [[Exact differential equation]] | + | * [[Complex differential equation|Complex]] |
− | * [[ | + | * Coupled{{\}}Decoupled |
+ | * [[Exact differential equation|Exact]] | ||
+ | * [[Homogeneous differential equation|Homogeneous]]{{\}}[[Non-homogeneous differential equation|Nonhomogeneous]] | ||
+ | {{endflatlist}} | ||
+ | | heading3 = Features | ||
+ | | content3 = | ||
+ | {{startflatlist}} | ||
+ | * [[Ordinary differential equation#Definitions|Order]] | ||
+ | * [[Differential operator|Operator]] | ||
+ | {{endflatlist}} | ||
+ | * [[Notation for differentiation|Notation]] | ||
+ | }} | ||
− | | | + | | list4name = processes |
− | | | + | | list4title = Relation to processes |
− | | | + | | list4 = |
− | * [[Difference equation|Difference | + | * [[Difference equation|Difference {{smaller|(discrete analogue)}}]] |
− | * [[Stochastic differential equation| | + | {{startflatlist}} |
+ | * [[Stochastic differential equation|Stochastic]] | ||
+ | ** [[Stochastic partial differential equation|Stochastic partial]] | ||
* [[Delay differential equation|Delay]] | * [[Delay differential equation|Delay]] | ||
+ | {{endflatlist}} | ||
− | |||
− | | | + | <!---------------------------- Solution -----------------------------> |
− | | | + | | heading5 = Solution |
− | | | + | |
− | * [[Picard–Lindelöf theorem | + | | list5name = existence and uniqueness |
+ | | list5title = Existence and uniqueness | ||
+ | | list5 = | ||
+ | * [[Picard–Lindelöf theorem|Picard–Lindelöf theorem <!--{{smaller|(existence/uniqueness)}}-->]] | ||
+ | * [[Peano existence theorem]] | ||
+ | * [[Carathéodory's existence theorem]] | ||
+ | * [[Cauchy–Kowalevski theorem]] | ||
+ | |||
+ | | list6name = solution | ||
+ | | list6title = General topics | ||
+ | | list6 = | ||
* [[Wronskian]] | * [[Wronskian]] | ||
* [[Phase portrait]] | * [[Phase portrait]] | ||
* [[Phase space]] | * [[Phase space]] | ||
− | * [[Lyapunov stability]] | + | * [[Lyapunov stability|Lyapunov]]{{\}}[[Asymptotic stability|Asymptotic]]{{\}}[[Exponential stability]] |
− | |||
− | |||
* [[Rate of convergence]] | * [[Rate of convergence]] | ||
− | * [[Power series solution of differential equations|Series | + | * {{nowrap|[[Power series solution of differential equations|Series]]{{\}}Integral solutions}} |
− | |||
* [[Numerical integration]] | * [[Numerical integration]] | ||
− | * [[Dirac | + | * [[Dirac delta function]] |
− | | | + | | list7name = solution methods |
− | | | + | | list7title = Solution methods |
− | | | + | | list7 = {{startflatlist}} |
* Inspection | * Inspection | ||
− | * [[ | + | * <!--(Char)-->[[Method of characteristics]] |
− | * [[ | + | * <br>[[Euler method|Euler]] |
+ | * [[Exponential response formula]] | ||
+ | * [[Finite difference method|Finite difference]] {{smaller|([[Crank–Nicolson method|Crank–Nicolson]])}} | ||
+ | * [[Finite element method|Finite element]] | ||
+ | ** [[Infinite element method|Infinite element]] | ||
+ | * [[Finite volume method|Finite volume]] | ||
+ | * [[Galerkin method|Galerkin]] | ||
+ | ** [[Petrov–Galerkin method|Petrov–Galerkin]] | ||
* [[Integrating factor]] | * [[Integrating factor]] | ||
* [[Integral transform]]s | * [[Integral transform]]s | ||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
* [[Perturbation theory]] | * [[Perturbation theory]] | ||
+ | * [[Runge–Kutta methods|Runge–Kutta]] | ||
+ | {{endflatlist}} | ||
+ | * [[Separation of variables]] | ||
+ | * [[Method of undetermined coefficients|Undetermined coefficients]] | ||
+ | * [[Variation of parameters]] | ||
− | |||
− | |||
− | |||
+ | <!---------------------------- People -------------------------------> | ||
+ | | list8name = people | ||
+ | | list8title = <div class="navbox-abovebelow" style="font-size:105%;padding:0.1em 0.2em;">People</div> | ||
+ | | list8 = {{startflatlist |style=padding-top:0.5em}} | ||
* [[Isaac Newton]] | * [[Isaac Newton]] | ||
+ | * [[Gottfried Leibniz]] | ||
* [[Leonhard Euler]] | * [[Leonhard Euler]] | ||
− | * [[ | + | * [[Émile Picard]] |
* [[Józef Maria Hoene-Wroński]] | * [[Józef Maria Hoene-Wroński]] | ||
* [[Ernst Lindelöf]] | * [[Ernst Lindelöf]] | ||
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* [[Phyllis Nicolson]] | * [[Phyllis Nicolson]] | ||
* [[Carl David Tolmé Runge]] | * [[Carl David Tolmé Runge]] | ||
− | * [[Martin | + | * [[Martin Kutta]] |
+ | {{endflatlist}} | ||
− | }}<noinclude>{{ | + | }}</includeonly><noinclude>{{Documentation}}</noinclude> |
Latest revision as of 08:26, 20 December 2020
Differential equations | |||||
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![]() Navier–Stokes differential equations used to simulate airflow around an obstruction. | |||||
Classification | |||||
Types
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Relation to processes |
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Solution | |||||
Existence and uniqueness |
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General topics |
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Solution methods
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This template includes collapsible lists.
- • To set it to display all lists when it appears (i.e. all lists expanded), use:
-
{{Differential equations |expanded=all}}
or, if enabled,{{Differential equations |all}}
(i.e. omitting "expanded=
").
- • To set it to display one particular list while keeping the remainder collapsed (i.e. hidden apart from their headings), use:
-
{{Differential equations |expanded=listname}}
or, if enabled,{{Differential equations |listname}}
- …where listname is one of the following (do not include any quotemarks):
- scope, types, processes, solution, "solution methods", people
- For example,
{{Differential equations |expanded=solution methods}}
or, if enabled,{{Differential equations |solution methods}}
The above documentation is transcluded from Template:Differential equations/doc. (edit | history) Editors can experiment in this template's sandbox (create | mirror) and testcases (create) pages. Please add categories to the /doc subpage. Subpages of this template. |