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Solving four coupled differential equations

Posted 2014年1月29日 GMT-5 01:43 Modeling Tools & Definitions, Parameters, Variables, & Functions Version 4.3b, Version 4.4 3 Replies

dnh37
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Hi,

There's an energy equation I need to minimize. This equation is the first equation on this page: www.ee.ucl.ac.uk/~rjames/modelling/constant-order/oned/

However if you follow that page then you realize that energy minimization problem ends up being four linear differential equations to solve. (The 7th set of equations on that page.)

Now, I can do this in Matlab, indeed that link above does it for the 1D case in Matlab. Now I want to get COMSOL to solve these four differential equations. I see that I can go New > 2D > Global ODEs and DAEs > Global Equation, and I can enter differential equation here, but this is a differential equation of one variable, f(u,ut,utt,t), not a set of coupled differential equations. How do I enter four coupled differential equations and have matlab solve them on some mesh?

Is there some tutorial online for how to solve coupled differential equations on 2D or 3D meshes? I fail to find one.

Thanks.

P.S. if you are interested, I'm trying to solve the "director" distribution in a liquid crystal (LC) sandwich.
"Director" is the unit vector that describes which direction the LC molecules point at any given point.
By "sandwich" I mean, glass-LC-glass, and I'm drawing a 2D slice through this and trying to solve the director distribution at each mesh point.
3 Replies Last Post 2014年8月20日 GMT-4 05:17
dnh37
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Posted: 1 decade ago 2014年1月29日 GMT-5 10:15
Also, is it generally true that to solve energy minimization problems of some physics over some area or volume, that you must convert it to coupled differential equations?

Searching "comsol energy minimization" etc yielded no general approaches nor specific code examples...
Also, is it generally true that to solve energy minimization problems of some physics over some area or volume, that you must convert it to coupled differential equations? Searching "comsol energy minimization" etc yielded no general approaches nor specific code examples...
Dan McLean
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Posted: 1 decade ago 2014年2月21日 GMT-5 17:14
dnh37,
I attach a simple file derived from a SHG example solution that shows laser pulse propagating through a sample. In the sample I introduce two coupled differential equations that represent excitation to an excited state (NS1) and relaxation back to the ground state (NS0). Additional coupled equations can be added.
dnh37, I attach a simple file derived from a SHG example solution that shows laser pulse propagating through a sample. In the sample I introduce two coupled differential equations that represent excitation to an excited state (NS1) and relaxation back to the ground state (NS0). Additional coupled equations can be added.
Pulkit Singh
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Posted: 1 decade ago 2014年8月20日 GMT-4 05:17
hi

dnh

if you had any break through, can u plz guide me on the same.

moreover i want to know how can i give variable inputs to the coefficients used in the differential equations.
hi dnh if you had any break through, can u plz guide me on the same. moreover i want to know how can i give variable inputs to the coefficients used in the differential equations.

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