Solving Coupled PDEs: A Comprehensive Guide

In summary, the conversation is about the concept of coupled PDEs and the speaker's struggle to understand it. They provide an example of a system and ask for clarification on how to write it as a pair of coupled PDEs. They also express their frustration with not being able to find a clear answer on this topic. They apologize for joining the forum only to ask questions and mention their plan to participate in other discussions after meeting a deadline. They ask if there is a protocol they should follow.
  • #1
Hazmitaz
3
0
Hello,

It has taken me a long time to try and figure out what a system of coupled PDEs actually IS-and I still can't get a straight answer.

For example I have a system:

[itex]\dot{M}[/itex]=-LvM

[itex]\dot{N}[/itex]=-Lv+wN

where here ,L, represents the lie derivative and M, N , v, w, are all elements of the sets of vector fields on a manifold. And I want to write this system as a pair of coupled PDEs with independent variables (x,t)[itex]\in[/itex]ℝxℝ.
I hope this question is clear and please answer sooner rather than later if you can.
 
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  • #2
Any thoughts at all-passing notions even would really help. Even if it's to say I'm making no sense or asking something trivial.

In all honesty I really do have this problem: what are coupled PDEs? I can't get a straight answer anywhere.

Although I am very new to Physics Forums-and apologise for joining just to inundate with questions-I plan, as soon as I'm out of my current deadline to join other threads-is there a protocal I've missed?
 

1. What are coupled partial differential equations (PDEs)?

Coupled PDEs are a system of two or more partial differential equations that are interconnected and affect each other's solutions. They are used to model complex physical phenomena, such as fluid flow, heat transfer, and electromagnetic fields.

2. What is the purpose of "Solving Coupled PDEs: A Comprehensive Guide"?

The purpose of this guide is to provide a comprehensive overview of techniques and methods for solving coupled PDEs. It covers both analytical and numerical methods, and provides step-by-step instructions and examples for solving various types of coupled PDEs.

3. What are some common approaches for solving coupled PDEs?

Some common approaches for solving coupled PDEs include separation of variables, method of characteristics, finite difference method, finite element method, and spectral methods. Each approach has its own advantages and limitations, and the choice of method depends on the specific problem being solved.

4. What are some challenges in solving coupled PDEs?

Solving coupled PDEs can be challenging due to the complexity of the equations and their interdependence. It may require advanced mathematical techniques and extensive computational resources. Additionally, finding an accurate and efficient solution can be difficult, and the solutions may be sensitive to small changes in the parameters or initial/boundary conditions.

5. How can I use the information in this guide to solve my own coupled PDE problem?

This guide provides a general framework for solving coupled PDEs, but each problem is unique and may require adaptation or combination of different methods. It is important to carefully study the problem and understand the underlying physical principles before choosing a solution method. The examples and step-by-step instructions in this guide can serve as a guide, but it is ultimately up to the user to apply the techniques to their specific problem.

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