System of DEs with different denominators

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In summary, the conversation discusses the process of solving a system of differential equations numerically. The equations have different denominators and the individual is unsure of how to approach this using Runge-Kutta. They also mention that the equations are partial, as they only depend on either dT/dx or dT/dt. Additionally, the person has limited knowledge in math and is seeking help in solving the problem.
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sebasbri
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system of DEs with different "denominators"

Hi,

Sorry in advance for the lack of knowledge of the techincal terms.

I am trying to solve a system of differential equations numerically, and I am not sure how to go about it. I've got 7 equations total; 5 of the form dT/dt = f(T1,T2,T3...) and 2 of the form dT/dx = f(T1,T2,T3...) .

***Note*** dT could be dT1, dT2, dT3...

How can I solve this numerically? I was looking at Runge-Kutta, but I'm not sure that I can since some equations have different "denominators".

Does anybody understand what I'm trying to ask? If you need more info, let me know.

I attached a pdf of the equations if that can help... Those equations will actually change (I just wrote them up really quickly, and I know that there are lots of mistakes in them) but it should give you a good idea of the problem. Some of the h coefficient are functions of T, m1 and m2 are functions of x.

Thanks for any kind of help
 

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  • #2
So these are partial differential equations? That is your functions depend upon the two independent variables x and t?
 
  • #3
Yes. I wasn't sure if you could call them partial because each equation only depends on dT/dx or dT/dt, not both at the same time.

As you probably suspect, math is NOT my forte. I am just starting a Masters in mech. eng. and my differential equations course was 3 years ago. I forgot everything I learned in that class as soon as I wrote the final ;) I do remember most of my numerical classes though (although I don't believe we spent much time on systems of differential equations).
HallsofIvy said:
So these are partial differential equations? That is your functions depend upon the two independent variables x and t?
 
Last edited:

What is a system of differential equations with different denominators?

A system of differential equations with different denominators is a set of equations that involve multiple variables and their derivatives, where each equation has a different denominator. These types of systems are often used to model real-world phenomena, such as population growth or chemical reactions.

How do you solve a system of differential equations with different denominators?

To solve a system of differential equations with different denominators, you can use the method of elimination or substitution. This involves manipulating the equations to eliminate one of the variables and then solving for the remaining variables. Alternatively, you can use numerical methods, such as Euler's method or Runge-Kutta methods, to approximate the solutions.

What are some applications of systems of differential equations with different denominators?

Systems of differential equations with different denominators have many applications in various fields, including physics, engineering, biology, and economics. They can be used to model complex systems, predict future behavior, and make informed decisions based on mathematical analysis.

Can a system of differential equations with different denominators have multiple solutions?

Yes, a system of differential equations with different denominators can have multiple solutions. In fact, many real-world problems have infinitely many solutions, and it is up to the scientist to determine which solution is the most appropriate for the given situation.

What are some techniques for analyzing systems of differential equations with different denominators?

There are several techniques for analyzing systems of differential equations with different denominators, including phase plane analysis, linearization, and stability analysis. These techniques help to understand the behavior of the system and make predictions about its long-term behavior.

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