Intelligent driver model - Revision history

2001:1620:2018:2A:2107:E4D3:EC21:B45C: /* Model definition */

2014-12-14T15:55:55Z

Model definition

← Older revision		Revision as of 17:55, 14 December 2014
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	~~The '''Lax–Wendroff method'''~~, ~~named after [[Peter Lax]]~~ and ~~[[Burton Wendroff]],~~ is a ~~[[numerical analysis\|numerical]] method for the solution of [[hyperbolic partial differential equation]]s, based on [[finite difference]]s~~. It is ~~second-order accurate in both space and time. This method is an example of [[temporal discretization\|explicit time integration]] where the function~~ that ~~defines governing equation~~ is ~~evaluated at the current time~~.		I would like to introduce myself to you, I am Andrew and my wife doesn't like it at all. Credit authorising is how she makes a living. Playing badminton is a factor that he is completely addicted to. Her family life in Ohio.<br><br>Also visit my webpage best psychics ([http://c045.danah.co.kr/home/index.php?document_srl=1356970&mid=qna Full Posting])

	~~Suppose one has an equation of the following form:~~

	~~: <math> \frac{\partial f(x,t)}{\partial t}=\frac{\partial g(f(x,t))}{\partial x}\,</math>~~

	~~where ''x'' and ''t'' are independent variables, and the initial state, ƒ(''x'', 0) is given.~~

	~~The first step~~ in ~~the Lax–Wendroff method calculates values for ƒ(''x'', ''t'') at half time steps, ''t''<sub>''n'' + 1/2</sub> and half grid points, ''x''<sub>''i'' + 1/2</sub>~~. ~~In the second step values at ''t''<sub>''n'' + 1</sub> are calculated using the data for ''t''~~<~~sub~~>~~''n''</sub> and ''t''~~<~~sub~~>~~''n'' + 1/2</sub>.~~

	~~First~~ (~~Lax) step~~:

	~~: <math> \cfrac{f_{i+1~~/~~2}^{n+1~~/~~2} - \cfrac{f_i^n+f_{i+1}^n}{2}}{(1/2) * \Delta t}=\cfrac{g_{i+1}^n - g_i^n}{\Delta x}~~.~~\,</math>~~

	~~Second step:~~

	~~: <math> \cfrac{f_i^{n+1} - f_i^n}{\Delta t}=\cfrac{g_{i+1/2}^{n+1/2} - g_{i-1/2}^{n+1/2}}{\Delta x}~~.~~\, </math>~~

	~~This method can be further applied to some systems of partial differential equations.~~

	~~==References==~~
	* {{ cite journal \| author = P.D Lax \| coauthors = B. Wendroff \| year = 1960 \| title = Systems of conservation laws \| journal = Commun. Pure Appl Math. \| volume = 13 \| pages = 217–237 \| doi = 10.1002/cpa.3160130205 \| issue = 2 }}
	* Michael J. Thompson, ''An Introduction to Astrophysical Fluid Dynamics'', Imperial College Press, London, 2006.
	*{{Cite book \| last1=Press \| first1=WH \| last2=Teukolsky \| first2=SA \| last3=Vetterling \| first3=WT \| last4=Flannery \| first4=BP \| year=2007 \| title=Numerical Recipes: The Art of Scientific Computing \| edition=3rd \| publisher=Cambridge University Press \| publication-place=New York \| isbn=978-0-521-88068-8 \| chapter=Section 20.1. ~~Flux Conservative Initial Value Problems \| chapter-url=http:~~/~~/apps.nrbook.com/empanel~~/index.~~html#pg~~=~~1040 \| page~~=~~1040}}~~

	~~{{Numerical PDE}}~~

	~~{{DEFAULTSORT:Lax-Wendroff Method}}~~
	~~[[Category:Numerical differential equations~~]]
	~~[[Category:Computational fluid dynamics]]~~


	~~{{mathapplied-stub}}~~

79.123.73.21: proper link

2013-11-17T13:08:19Z

proper link

← Older revision		Revision as of 15:08, 17 November 2013
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	~~Hi there~~, ~~I am Sophia~~. ~~Mississippi~~ is ~~exactly~~ where ~~his house~~ is. ~~Invoicing~~ is ~~what I do~~. ~~I am truly fond of handwriting but I can~~'t ~~make it my profession truly~~.<br><br>~~Feel free to visit my blog tarot card readings~~ (~~[http~~://~~www~~.~~publicpledge~~.~~com~~/~~blogs~~/~~post/7034~~ http://~~www~~.~~publicpledge~~.com])		The '''Lax–Wendroff method''', named after [[Peter Lax]] and [[Burton Wendroff]], is a [[numerical analysis\|numerical]] method for the solution of [[hyperbolic partial differential equation]]s, based on [[finite difference]]s. It is second-order accurate in both space and time. This method is an example of [[temporal discretization\|explicit time integration]] where the function that defines governing equation is evaluated at the current time.

			Suppose one has an equation of the following form:

			: <math> \frac{\partial f(x,t)}{\partial t}=\frac{\partial g(f(x,t))}{\partial x}\,</math>

			where ''x'' and ''t'' are independent variables, and the initial state, ƒ(''x'', 0) is given.

			The first step in the Lax–Wendroff method calculates values for ƒ(''x'', ''t'') at half time steps, ''t''<sub>''n'' + 1/2</sub> and half grid points, ''x''<sub>''i'' + 1/2</sub>. In the second step values at ''t''<sub>''n'' + 1</sub> are calculated using the data for ''t''<sub>''n''</sub> and ''t''<sub>''n'' + 1/2</sub>.

			First (Lax) step:

			: <math> \cfrac{f_{i+1/2}^{n+1/2} - \cfrac{f_i^n+f_{i+1}^n}{2}}{(1/2) * \Delta t}=\cfrac{g_{i+1}^n - g_i^n}{\Delta x}.\,</math>

			Second step:

			: <math> \cfrac{f_i^{n+1} - f_i^n}{\Delta t}=\cfrac{g_{i+1/2}^{n+1/2} - g_{i-1/2}^{n+1/2}}{\Delta x}.\, </math>

			This method can be further applied to some systems of partial differential equations.

			==References==
			* {{ cite journal \| author = P.D Lax \| coauthors = B. Wendroff \| year = 1960 \| title = Systems of conservation laws \| journal = Commun. Pure Appl Math. \| volume = 13 \| pages = 217–237 \| doi = 10.1002/cpa.3160130205 \| issue = 2 }}
			* Michael J. Thompson, ''An Introduction to Astrophysical Fluid Dynamics'', Imperial College Press, London, 2006.
			*{{Cite book \| last1=Press \| first1=WH \| last2=Teukolsky \| first2=SA \| last3=Vetterling \| first3=WT \| last4=Flannery \| first4=BP \| year=2007 \| title=Numerical Recipes: The Art of Scientific Computing \| edition=3rd \| publisher=Cambridge University Press \| publication-place=New York \| isbn=978-0-521-88068-8 \| chapter=Section 20.1. Flux Conservative Initial Value Problems \| chapter-url=http://apps.nrbook.com/empanel/index.html#pg=1040 \| page=1040}}

			{{Numerical PDE}}

			{{DEFAULTSORT:Lax-Wendroff Method}}
			[[Category:Numerical differential equations]]
			[[Category:Computational fluid dynamics]]


			{{mathapplied-stub}}

188.220.171.33 at 20:40, 11 November 2010

2010-11-11T20:40:58Z

New page

Hi there, I am Sophia. Mississippi is exactly where his house is. Invoicing is what I do. I am truly fond of handwriting but I can't make it my profession truly.<br><br>Feel free to visit my blog tarot card readings ([http://www.publicpledge.com/blogs/post/7034 http://www.publicpledge.com])