Numerical Solutions to Coupled ODEs with Boundry Values at Opposite Ends

In summary, the conversation is about trying to solve a system of coupled non-linear first order ODEs with boundary conditions at opposite ends in Python. The person is looking for strategies and libraries that can help with this problem. One suggestion is to use MATLAB with the "bvp" function. Another suggestion is to use COMSOL, which is a user-friendly software that can numerically solve systems of non-linear and coupled ODEs and PDEs.
  • #1
jsalvati
2
0
I am trying to model a packed bed distillation column for a binary liquid in Python. Unfortunately, when I set up my system, I end up with a system of coupled non-linear first order ODEs with boundary conditions at opposite ends (feed conditions and exit conditions), and I do not know how to solve this sort of problem. I know how to solve coupled non-linear ODEs with boundary conditions at the same end, and SciPy has a coupled ODE solver in any case, but I do not know any strategies for solving coupled ODEs with boundary conditions at different ends.

Can anyone recommend a source for reading up on strategies? Or know of any libraries with such solvers (esp. in Python)? This is mostly for entertainment, so if this is an ultra difficult problem, I am willing to give up.
 
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  • #2
that is the boundary value problem
matlab could solve it
the order is "bvp" or something like that
 
  • #3
COMSOL is a great software application I use to solve systems of non-linear and coupled ODE's and PDE's.

It's very user-friendly, and it uses finite element method to numerically solve the systems. Not sure if you have access to it, but I figured I'd suggest it if you could use it.
 

1. What are coupled ODEs?

Coupled ODEs (Ordinary Differential Equations) are a set of two or more equations that are connected and dependent on each other. This means that the solution to one equation will affect the solution of the other equations in the set.

2. How are numerical solutions to coupled ODEs calculated?

Numerical solutions to coupled ODEs are calculated using numerical methods such as Euler's method, Runge-Kutta method, or finite difference methods. These methods involve breaking down the coupled ODEs into smaller, simpler equations and solving them iteratively.

3. What are boundary values at opposite ends?

Boundary values at opposite ends refer to the boundary conditions of a coupled ODEs problem. These conditions are specified at the two ends of the domain and are used to determine the solution of the coupled ODEs within that domain.

4. Why are numerical solutions important for coupled ODEs with boundary values at opposite ends?

Numerical solutions are important for coupled ODEs with boundary values at opposite ends because they provide a way to approximate the solution without having to solve the equations analytically, which can be difficult or even impossible in some cases. They also allow for more complex and realistic systems to be modeled and analyzed.

5. What are some real-world applications of coupled ODEs with boundary values at opposite ends?

Coupled ODEs with boundary values at opposite ends have many real-world applications, such as in physics, engineering, biology, and economics. They can be used to model and analyze systems such as heat transfer, population dynamics, chemical reactions, and financial markets.

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