Difference between revisions of "Template:Differential equations"
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imported>Sardanaphalus (bodyclass, titleclass/style, image/caption, headingclass/style, list/titlestyle, expanded; listnames (including list3name/title); subsidebars; combined lists 3 and 4; removed generic linking; Collapsible lists option, includeonly) |
imported>Chongkian (match article name) |
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| titlestyle = display:block;margin-bottom:0.2em; | | titlestyle = display:block;margin-bottom:0.2em; | ||
| title = [[Differential equation]]s | | title = [[Differential equation]]s | ||
| − | | image = [[File: | + | | image = [[File:Navier_Stokes_Laminar.svg|235px|Navier–Stokes differential equations used to simulate airflow around an obstruction]] |
| captionstyle = padding-bottom:0.25em; | | captionstyle = padding-bottom:0.25em; | ||
| caption = [[Navier–Stokes equations|Navier–Stokes differential equations]] used to simulate airflow around an obstruction. | | caption = [[Navier–Stokes equations|Navier–Stokes differential equations]] used to simulate airflow around an obstruction. | ||
| Line 53: | Line 53: | ||
* [[Ordinary differential equation|Ordinary]] | * [[Ordinary differential equation|Ordinary]] | ||
* [[Partial differential equation|Partial]] | * [[Partial differential equation|Partial]] | ||
| − | * [[Differential algebraic | + | * [[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]] | ||
| Line 67: | Line 67: | ||
* Coupled{{\}}Decoupled | * Coupled{{\}}Decoupled | ||
* [[Exact differential equation|Exact]] | * [[Exact differential equation|Exact]] | ||
| − | * [[Homogeneous differential | + | * [[Homogeneous differential equation|Homogeneous]]{{\}}[[Non-homogeneous differential equation|Nonhomogeneous]] |
{{endflatlist}} | {{endflatlist}} | ||
| heading3 = Features | | heading3 = Features | ||
| content3 = | | content3 = | ||
{{startflatlist}} | {{startflatlist}} | ||
| − | * [[ | + | * [[Ordinary differential equation#Definitions|Order]] |
| − | |||
* [[Differential operator|Operator]] | * [[Differential operator|Operator]] | ||
{{endflatlist}} | {{endflatlist}} | ||
| Line 85: | Line 84: | ||
{{startflatlist}} | {{startflatlist}} | ||
* [[Stochastic differential equation|Stochastic]] | * [[Stochastic differential equation|Stochastic]] | ||
| + | ** [[Stochastic partial differential equation|Stochastic partial]] | ||
* [[Delay differential equation|Delay]] | * [[Delay differential equation|Delay]] | ||
{{endflatlist}} | {{endflatlist}} | ||
| Line 91: | Line 91: | ||
<!---------------------------- Solution -----------------------------> | <!---------------------------- Solution -----------------------------> | ||
| heading5 = Solution | | heading5 = Solution | ||
| + | |||
| + | | 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 | | list6name = solution | ||
| list6title = General topics | | list6title = General topics | ||
| − | | list6 = | + | | list6 = |
| − | |||
* [[Wronskian]] | * [[Wronskian]] | ||
| − | |||
* [[Phase portrait]] | * [[Phase portrait]] | ||
* [[Phase space]] | * [[Phase space]] | ||
| − | |||
* [[Lyapunov stability|Lyapunov]]{{\}}[[Asymptotic stability|Asymptotic]]{{\}}[[Exponential stability]] | * [[Lyapunov stability|Lyapunov]]{{\}}[[Asymptotic stability|Asymptotic]]{{\}}[[Exponential stability]] | ||
* [[Rate of convergence]] | * [[Rate of convergence]] | ||
* {{nowrap|[[Power series solution of differential equations|Series]]{{\}}Integral solutions}} | * {{nowrap|[[Power series solution of differential equations|Series]]{{\}}Integral solutions}} | ||
| − | |||
* [[Numerical integration]] | * [[Numerical integration]] | ||
* [[Dirac delta function]] | * [[Dirac delta function]] | ||
| − | |||
| list7name = solution methods | | list7name = solution methods | ||
| − | | list7title = | + | | list7title = Solution methods |
| list7 = {{startflatlist}} | | list7 = {{startflatlist}} | ||
* Inspection | * Inspection | ||
* <!--(Char)-->[[Method of characteristics]] | * <!--(Char)-->[[Method of characteristics]] | ||
| − | * <br | + | * <br>[[Euler method|Euler]] |
| + | * [[Exponential response formula]] | ||
* [[Finite difference method|Finite difference]] {{smaller|([[Crank–Nicolson method|Crank–Nicolson]])}} | * [[Finite difference method|Finite difference]] {{smaller|([[Crank–Nicolson method|Crank–Nicolson]])}} | ||
* [[Finite element method|Finite element]] | * [[Finite element method|Finite element]] | ||
| + | ** [[Infinite element method|Infinite element]] | ||
* [[Finite volume method|Finite volume]] | * [[Finite volume method|Finite volume]] | ||
* [[Galerkin method|Galerkin]] | * [[Galerkin method|Galerkin]] | ||
| + | ** [[Petrov–Galerkin method|Petrov–Galerkin]] | ||
* [[Integrating factor]] | * [[Integrating factor]] | ||
* [[Integral transform]]s | * [[Integral transform]]s | ||
| Line 126: | Line 132: | ||
* [[Separation of variables]] | * [[Separation of variables]] | ||
* [[Method of undetermined coefficients|Undetermined coefficients]] | * [[Method of undetermined coefficients|Undetermined coefficients]] | ||
| + | * [[Variation of parameters]] | ||
| Line 131: | Line 138: | ||
| list8name = people | | list8name = people | ||
| list8title = <div class="navbox-abovebelow" style="font-size:105%;padding:0.1em 0.2em;">People</div> | | list8title = <div class="navbox-abovebelow" style="font-size:105%;padding:0.1em 0.2em;">People</div> | ||
| − | | list8 = {{startflatlist|padding-top:0.5em}} | + | | list8 = {{startflatlist |style=padding-top:0.5em}} |
* [[Isaac Newton]] | * [[Isaac Newton]] | ||
| + | * [[Gottfried Leibniz]] | ||
* [[Leonhard Euler]] | * [[Leonhard Euler]] | ||
* [[Émile Picard]] | * [[Émile Picard]] | ||
| Line 142: | Line 150: | ||
* [[Phyllis Nicolson]] | * [[Phyllis Nicolson]] | ||
* [[Carl David Tolmé Runge]] | * [[Carl David Tolmé Runge]] | ||
| − | * [[Martin | + | * [[Martin Kutta]] |
{{endflatlist}} | {{endflatlist}} | ||
}}</includeonly><noinclude>{{Documentation}}</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. | |||||
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Types
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Relation to processes |
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| Solution | |||||
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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. |