The Bender and Orszag analog for PDE

In summary, Ll.N. Trefethen and M. Embree's "Spectral Methods in MATLAB" is a useful resource for anyone looking to learn about perturbation theory and asymptotic methods for PDEs with a focus on practical applications.
  • #1
Llewlyn
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The "Bender and Orszag" analog for PDE

There is a famous book written by Bender and Orszag named "Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory" which explains how to obtain approximated solutions for ordinary differential equation. Well, now I'm looking for something similar: a book of perturbation theory and asymptotic methods for PDE. There are many of course and I'd like something which focuses much more on application than mathematical rigor, but without being useless. Just like the "Bender-Orszag".

Do you know anything?

Ll.
 
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  • #2
N. Trefethen and M. Embree's book "Spectral Methods in MATLAB" might be a good option. It provides a general overview of numerical methods for solving PDEs, as well as detailed explanations of the various techniques, such as Fourier and Chebychev methods, and how they are implemented in MATLAB. Additionally, it includes many examples of practical applications of these techniques.
 

1. What is the Bender and Orszag analog for PDE?

The Bender and Orszag analog for PDE (Partial Differential Equation) is a mathematical technique used to solve nonlinear partial differential equations. It is based on the concept of perturbation theory, where the solution to a complex problem is approximated by breaking it down into simpler, solvable parts.

2. How does the Bender and Orszag analog work?

The Bender and Orszag analog works by converting a nonlinear partial differential equation into a set of linear equations, which are then solved using perturbation theory. This involves iterating over the equations multiple times, each time adding a small perturbation term to the previous solution until the desired level of accuracy is achieved.

3. What types of problems can the Bender and Orszag analog solve?

The Bender and Orszag analog can solve a wide range of problems, including fluid dynamics, quantum mechanics, and heat transfer. It is especially useful for problems that involve nonlinear partial differential equations, which are difficult to solve using traditional methods.

4. What are the advantages of using the Bender and Orszag analog?

One of the main advantages of using the Bender and Orszag analog is its ability to handle complex, nonlinear problems that would be difficult or impossible to solve using traditional methods. It also allows for a more systematic approach to solving these problems, making it easier to obtain accurate solutions.

5. Are there any limitations to the Bender and Orszag analog?

While the Bender and Orszag analog is a powerful tool for solving nonlinear PDEs, it does have some limitations. It may not work well for problems with highly irregular or chaotic behavior, and the accuracy of the solutions depends on the choice of perturbation terms. Additionally, the method can become computationally intensive for complex problems with many iterations required.

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