Solving two simultaneous differential equations and need to plot them wrt to time .

[nkarna]

Hello all,

I am currently trying to solve two simultaneous equations and they are dependent on multiple variables . I could not solve them and simultaneously and also have to use the output of them to make an input for other and try to iterate and optimise it . I have removed all the units as I was facing problem with a couple of them . so just I m working with plain numbers .

Can some one please help me ..

I am kind of on intermediate level in mathcad prime

Nitin

[RichardJ]

Sorry, that's a Prime 3.1 file, so I can't read it. If you post a pdf maybe I (or someone else that does not have Prime 3.1) can help.

[nkarna]

Thanks a lot for the reply , please find the attached xps file for the same

[RichardJ]

I assume the two equations you want to solve are M(h) and U(h). You have two definitions of M(h). For the first, you define it as d/dt(h), but since h is a constant that's 0. Your definition of U(h) includes an undefined variable T, and d/dt(omega_rel), but you have defined omega_rel as a constant, not a function of t, so the derivative is 0. Even if you define the variable T and fix the definition of omega_rel the variable h will not appear on  the rhs of the equation though, so the value returned by U(h) will be constant. Lastly, you are using odesolve in the solve block, but you do not have differential equations.

Please specify exactly the form of the two equations you wish to solve, and which two variables you wish to solve for.

[nkarna]

Thanks Richard.

My two equations to be solved are dh/dt and the other is the total T = I d(omega)/dt and vairables are h and t.

I have taken a initial  value of h  to calculate all the parameters including T . I am actually trying to solve the differential equations for h and omega rel. 

after solving then use the updated T to computer another function D till that function D converges .

Later I need to plot for T and t . Could you please help me in getting to complete the worksheet.

[RichardJ]

The document says it was created using Mathcad Express. Do you have Mathcad Express, or the full version of Mathcad Prime?

[nkarna]

I have mathcad Prime 3.1 full version for 30 days . and also have access to mathcad- 15

[RichardJ]

Then you would be much better off doing this in Mathcad 15. More people on these forums would be able to read your worksheet, and you would still be able to use it after 30 days. You can of course still use Prime after 30 days, but only as the express version which does not support many things, one of which is solving systems of DEs.

Anyway, I can't figure out what you are trying to do. You say you want to solve for omega_rel, but you have a definition of omega_rel in terms of omega_0, t, and t_0, so what's to solve for?

[nkarna]

Yes, because for each value of h , there wil be different values of omega_rel, and it also changes with respect to time .

So omega_rel is dependent of multiple factors like h,t, Kp etc. i am actually trying to build a mathematical model based on a paper.

[RichardJ]

Sorry, but your document is way too confusing for me to get anywhere with it. It would be tough with a worksheet I could edit, but with a static document there is no chance. You have a definition of omega_rel that depends only on omega_0, t, and t_0. So how is that definition compatible with your assertion that it depends on h and Kp? Another example is your definitions of Th and Ta. You have theta as a variable of integration, but nothing in the kernel depends on theta. In fact, there is no indication anywhere in your worksheet of how theta is related to any of the other variables or functions. You have solve blocks with no constraints in them, so what are they supposed to solve for? I get the impression that you think Mathcad will just infer relationships between your various numerical definitions, but it won't. A numerical definition just creates a variable with an assigned value. Nothing more. So as you have it, h is a constant. dh/dt is therefore 0. If there are supposed to be relationships between variables and functions you have to explicitly define them. Mathcad can't do it for you, and I am not familiar enough with what you are trying to do to do it for you.

[nkarna]

May be i was expecting too much from mathcad , Now i understood I have attached a word document which says wat my goal is , and i was just using mathcad as a solver I have attached my dcument here. may be this could give some idea and i can get help

ALso I was trying to plot a function

I could plot this in mathcad-15 , but in mathcad prime i was not succesfull

[RichardJ]

There's still missing information. Take your first equation, with the integral. The variable of integration is z, but it does not say what z represents. Since it's not a variable in mu(T), the integral evaluates to d/mu(T). But since it's multiplied by 1/d we just get mu_bar=mu(T). It seems unlikely to me that someone would write a trivially simple equation in the form of an integral, so there is some key piece of information that is missing. It also does not explain what theta is, even though it's a variable of integration. Is something in the kernel of those integrals actually supposed to depend on theta? If so, which one(s), and what is the dependence? Maybe you are familiar enough with the science/engineering this describes that you know what all these variables mean, but I don't, and there is no chance a software package is going to know. Without all the missing information there is no way to even enter everything into Mathcad in a meaningful way.

If you have Mathcad 15, why are you using the trial version of Prime to do this? Mathcad 15 is way more powerful than Mathcad Prime, so is there some specific reason you have chosen Mathcad Prime?