Materials on modelling phenomena with ODE/PDE

In summary, the conversation is about finding guidance and resources for modeling real world phenomena using ODE/PDE/SDE equations. The person is specifically interested in the field of systems biology and has questions about formulating and verifying models. The suggested book is "Transport Phenomena" by Bird, Stewart, and Lightfoot.
  • #1
Excoriate
9
0
Hi,

I am looking for some guidance w.r.t modelling real world phenomena using ODE/PDE/SDE type equations. Are there books which go into the issues of modelling real world phenomena with these sorts of equations?

Thanks in advance,

Excor.
 
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  • #2
What type of modeling are you looking into? Thermal modeling, electromagnetics, stress, ... etc.

Please do not say "ALL" as no book covers all of the information.

The more specific your question is the better the answer will be.

Thanks
Matt
 
  • #3
Well I am more looking for general principles but I am primarily interested in the area of systems biology atm.

The questions I am interested in are things like:

1) How does one go about formulating a model?
2) How does one verify that the model is correct?
 
  • #4
The best book that I can recommend is "Transport Phenomena" by Bird, Stewart, and Lightfoot.

Thanks
Matt
 
  • #5
Thanks I will take a look :-).
 

FAQ: Materials on modelling phenomena with ODE/PDE

What are ODEs and PDEs?

ODEs (Ordinary Differential Equations) and PDEs (Partial Differential Equations) are mathematical equations that describe the relationships between variables in a system. ODEs involve a single independent variable, while PDEs involve multiple independent variables.

Why do scientists use ODEs and PDEs in modelling phenomena?

ODEs and PDEs are used in modelling phenomena because they allow for the quantitative analysis and prediction of complex systems. They can also be used to understand the behavior of physical, chemical, and biological processes.

What is the difference between analytical and numerical solutions of ODEs and PDEs?

Analytical solutions involve finding a closed-form solution to the equation, while numerical solutions use computational methods to approximate the solution. Analytical solutions are often more accurate but can only be found for simple equations, while numerical solutions can be applied to more complex systems.

Can ODEs and PDEs be used to model real-world phenomena?

Yes, ODEs and PDEs are commonly used in scientific research to model and understand real-world phenomena, such as weather patterns, population dynamics, and chemical reactions. These equations can also be applied to engineering problems, such as predicting the behavior of structures and systems.

What are some challenges in using ODEs and PDEs to model phenomena?

One challenge is that many real-world phenomena are highly complex and cannot be accurately represented by simple equations. Additionally, the accuracy of the model depends on the accuracy of the initial conditions and parameters used. It can also be difficult to find analytical solutions for more complex systems, requiring the use of numerical methods.

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