**You are now following this question**

- You will see updates in your followed content feed.
- You may receive emails, depending on your communication preferences.

# why does pdepe adopt Petrov-Galerkin?

2 views (last 30 days)

Show older comments

feynman feynman
on 13 Feb 2024

##### 19 Comments

Torsten
on 13 Feb 2024

feynman feynman
on 13 Feb 2024

creators of pdepe are from mathworks, so I asked here :)

Torsten
on 13 Feb 2024

Edited: Torsten
on 13 Feb 2024

creators of pdepe are from mathworks, so I asked here :)

No. Responsible for the theoretical approach are the authors of the article:

[1] Skeel, R. D. and M. Berzins, "A Method for the Spatial Discretization of Parabolic Equations in One Space Variable," SIAM Journal on Scientific and Statistical Computing, Vol. 11, 1990, pp.1–32.

TMW won't be able to help in this respect.

feynman feynman
on 13 Feb 2024

right, I meant there must be good reason for mathworks to decide to adopt their Petrov-Galerkin?

feynman feynman
on 13 Feb 2024

Torsten
on 13 Feb 2024

Different university chairs propagate different methods - just consider all the methods used in codes for ordinary differential equations (BDF, Runge-Kutta, Extrapolation, Multistep,...).

"pdepe" is a stand-alone program to solve parabolic-elliptic PDEs in one spatial dimension. So why should the method used not differ from the one of the PDE Toolbox (or to whatever "solvepde" belongs) ?

feynman feynman
on 15 Feb 2024

Edited: feynman feynman
on 15 Feb 2024

feynman feynman
on 15 Feb 2024

Edited: feynman feynman
on 15 Feb 2024

Thanks for the tips

Torsten
on 15 Feb 2024

Edited: Torsten
on 15 Feb 2024

feynman feynman
on 15 Feb 2024

Torsten
on 15 Feb 2024

Edited: Torsten
on 15 Feb 2024

It cannot solve hyperbolic pdes because the f-term should not equal 0. Further, you have to specify two boundary conditions for each equation, and for equations of hyperbolic type you need only one. So one boundary condition will be wrong or at most artificial.

Why do you want a code force to solve hyperbolic equations if its name already indicates that it is created for the parabolic-elliptic type ?

If you are in need to solve hyperbolic PDEs, use CLAWPACK:

feynman feynman
on 16 Feb 2024

Edited: feynman feynman
on 16 Feb 2024

Torsten
on 16 Feb 2024

Edited: Torsten
on 16 Feb 2024

For pdepe, I don't know if periodic boundary conditions are allowed but if so PDEs having only first order spatial derivatives can also be solved.

Periodic boundary conditions are not possible with pdepe.

As said, setting up a problem with only first-order derivatives is technically possible. But you have to assume a second boundary condition that is mathematically incorrect. And usually - because the first derivative is in essence approximated by a central difference quotient - the results won't be stable.

feynman feynman
on 26 Feb 2024

I wonder if clawpack doesn't work in windows?

feynman feynman
on 26 Feb 2024

but their Installation Prerequisites says it only works in

- Linux
- Mac OS X

Torsten
on 26 Feb 2024

Edited: Torsten
on 26 Feb 2024

I didn't know - thanks for the info. Maybe you could try Cygwin.

When I worked with Clawpack, I just used the FORTRAN files together with mingw under Windows. But the software has grown ...

### Answers (0)

### See Also

### Categories

### Tags

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!**An Error Occurred**

Unable to complete the action because of changes made to the page. Reload the page to see its updated state.

Select a Web Site

Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .

You can also select a web site from the following list

How to Get Best Site Performance

Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.

Americas

- América Latina (Español)
- Canada (English)
- United States (English)

Europe

- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)

- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)

Asia Pacific

- Australia (English)
- India (English)
- New Zealand (English)
- 中国
- 日本Japanese (日本語)
- 한국Korean (한국어)