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Complex differential equation
Posted 16 juil. 2016, 15:01 UTC−4 1 Reply
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Hello,
I am a new user of Comsol and I try to solve this differential equation :
d''u/dz'' * (1+k*Sin(u)^2)*(1/pi)^2+ (d'u/dz')^2 * (sin(u)*cos(u)*(1/pi)^2+v*sin(u)*cos(u)=0
where:
k and v are constants and u is a function of z, while the range of z is : 0<z<1.
also : u(0)=0 and u(1)=pi/2
How can I solve it ?
Thanks
I am a new user of Comsol and I try to solve this differential equation :
d''u/dz'' * (1+k*Sin(u)^2)*(1/pi)^2+ (d'u/dz')^2 * (sin(u)*cos(u)*(1/pi)^2+v*sin(u)*cos(u)=0
where:
k and v are constants and u is a function of z, while the range of z is : 0<z<1.
also : u(0)=0 and u(1)=pi/2
How can I solve it ?
Thanks
1 Reply Last Post 25 juil. 2016, 14:31 UTC−4
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Posted:
8 years ago
Hello Asi,
Your equation is a perfect candidate for what at COMSOL we call "Equation-based modeling". Admittedly that terminology is not terribly descriptive since all modeling in COMSOL consists in the software solving equations, of course. What we mean by "equation-based modeling" is that the user gets to specify his or her own equations from scratch as opposed to using one of the pre-implemented equations or modifying one. This feature comes in handy when you need to solve an unusual equation like this one.
If you have never used equation-based modeling in COMSOL a great starting point is the Reference Guide, version 5.2a, Chapter 16. You will find several tutorials on the topic, with step-by-step instructions in the Applications Libraries (accessed through the File menu in COMSOL). In particular, since your model is going to be 1D, I would recommend you read the pdf file for the Black-Scholes Equation application.
Best,
Jeff
PS: There seems to be a missing parenthesis (or an extra one) in your equation.
Your equation is a perfect candidate for what at COMSOL we call "Equation-based modeling". Admittedly that terminology is not terribly descriptive since all modeling in COMSOL consists in the software solving equations, of course. What we mean by "equation-based modeling" is that the user gets to specify his or her own equations from scratch as opposed to using one of the pre-implemented equations or modifying one. This feature comes in handy when you need to solve an unusual equation like this one.
If you have never used equation-based modeling in COMSOL a great starting point is the Reference Guide, version 5.2a, Chapter 16. You will find several tutorials on the topic, with step-by-step instructions in the Applications Libraries (accessed through the File menu in COMSOL). In particular, since your model is going to be 1D, I would recommend you read the pdf file for the Black-Scholes Equation application.
Best,
Jeff
PS: There seems to be a missing parenthesis (or an extra one) in your equation.