/sci/ - Science & Math » Thread #10956163

14KiB, 306x462, 978-3-662-02661-8.jpg

View Same Google iqdb SauceNAO

Partial Differential Equations

Terry Tao Sun 08 Sep 17:14:38 2019 No.10956163 View Reply Original Report

Quoted By: >>10956187 >>10956645 >>10956693 >>10956756

How do we solve PDEs that we can't reduce to ODEs? Is category theory the key?

Anonymous

Anonymous Sun 08 Sep 2019 17:15:11 No.10956164 Report

Quoted By: >>10956182

>How do we solve PDEs that we can't reduce to ODEs?
What have you tried?

Terry Tao

Terry Tao Sun 08 Sep 2019 17:23:19 No.10956182 Report

Quoted By: >>10956185 >>10956746

>>10956164
Separation of variables, method of characteristics, change of variables, and lie group method

Anonymous

Anonymous Sun 08 Sep 2019 17:24:12 No.10956185 Report

Quoted By: >>10956189

>>10956182
>separation of variables
>change of variables
That`s literally reducing to an ODE.

Anonymous

Anonymous Sun 08 Sep 2019 17:25:09 No.10956187 Report

Quoted By: >>10956195

>>10956163
Either non-linear functional analysis tricks, numerical aproximations or other kinds of tricks.
That's basically PDE as a field.
Like, every equation is a special snowflake that you must mostly study on it's own (there are general classes of equations, bit they are obviously standins for the equations actually care about)

Anonymous

Anonymous Sun 08 Sep 2019 17:25:19 No.10956188 Report

Quoted By:

fixed point iteration

Terry Tao

Terry Tao Sun 08 Sep 2019 17:25:25 No.10956189 Report

Quoted By:

>>10956185
Yeah I tried it and couldn't do it

Terry Tao

Terry Tao Sun 08 Sep 2019 17:27:22 No.10956195 Report

Quoted By: >>10956707 >>10956766

>>10956187
There must be some underlying structure we haven't understood yet. How could something so fundamental to nature not have a general solution method. I'm not asking for it to be easy, but it should at least be possible.

Anonymous

Anonymous Sun 08 Sep 2019 20:09:06 No.10956645 Report

Quoted By:

>>10956163
finite element method

Anonymous

Anonymous Sun 08 Sep 2019 20:25:05 No.10956693 Report

Quoted By:

>>10956163
https://en.wikipedia.org/wiki/Variation_of_parameters

Anonymous

Anonymous Sun 08 Sep 2019 20:30:24 No.10956707 Report

Quoted By:

>>10956195
Why would fundamental things require general methods?

Anonymous

Anonymous Sun 08 Sep 2019 20:50:56 No.10956746 Report

Quoted By: >>10956758

>>10956182
i dont think you *actually* tried the lie group method (i.e. analyzing the lie group and lie algebra associated to the symmetries of the pde). it's the only honest method we have in nonlinear pdes. everything else is numerical analysis (unless youre gromov tier genius doing that h principle shit)

Anonymous

Anonymous Sun 08 Sep 2019 20:54:21 No.10956756 Report

Quoted By:

>>10956163
Because math dumb

Anonymous

Anonymous Sun 08 Sep 2019 20:55:23 No.10956758 Report

Quoted By: >>10956779

>>10956746

How do you think making a fool of yourself by permanently exposing your intentions would be a good idea?

Anonymous

Anonymous Sun 08 Sep 2019 20:56:26 No.10956761 Report

Quoted By:

The way I do it, I set all variables to be the same, like x, and then solve. Usually it's good enough.

Anonymous

Anonymous Sun 08 Sep 2019 20:57:32 No.10956766 Report

Quoted By:

>>10956195
>How could something so fundamental to nature not have a general solution method
If there isn't a general method even for finding polynomial zeroes, why would there be one for differential equations?

Anonymous

Anonymous Sun 08 Sep 2019 20:59:58 No.10956779 Report

Quoted By:

>>10956758
lolwut

Anonymous

Anonymous Sun 08 Sep 2019 22:20:04 No.10956999 Report

Quoted By:

finite difference methods with a really really really small time and space steps

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches