/sci/ - Science & Math » Thread #11336894

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Anonymous Mon 27 Jan 19:17:28 2020 No.11336894 View Reply Original Report

Quoted By: >>11336954 >>11336985 >>11337009 >>11339253 >>11339271 >>11339634 >>11339824 >>11339844

Can any differential equation be solved by applying Laplace Transform. Is this method OP?

Anonymous

Anonymous Mon 27 Jan 2020 19:28:18 No.11336920 Report

Quoted By:

This question sounds like a troll but if it isnt then ur retarded or watched one Khan academy video on diffeq. You can only solve a very niche set of ODEs that are even able to be transformed one-to-one

Anonymous

Anonymous Mon 27 Jan 2020 19:39:34 No.11336954 Report

Quoted By: >>11340401

>>11336894
not any differential equation, just specialized forms.

the actual OP method is Dormand and Prince (4,5) embedded numerical method with dense output. Can construct a solution to arbitrary precision and runs with minimal computational cost for the convergence rate.

Anonymous

Anonymous Mon 27 Jan 2020 19:56:50 No.11336985 Report

Quoted By:

>>11336894
>Can any differential equation be solved by applying Laplace Transform
no
>Is this method OP
LT is still OP but also based

Anonymous

Anonymous Mon 27 Jan 2020 20:04:22 No.11337009 Report

Quoted By:

>>11336894
>Can any differential equation be solved by applying Laplace Transform
no.

Anonymous

Anonymous Mon 27 Jan 2020 20:04:36 No.11337012 Report

Quoted By: >>11337950

>not solving everything with the finite element method

Anonymous

Anonymous Mon 27 Jan 2020 23:58:33 No.11337607 Report

Quoted By: >>11337611 >>11337667 >>11339760

since OP's question has a trivial answer,

what is the best non numerical way to solve as much types of ODE's as possible?

approximate/asymptotic solutions are acceptable if they guarantee they are good ones

Anonymous

Anonymous Mon 27 Jan 2020 23:59:25 No.11337611 Report

Quoted By:

>>11337607
variation of parameters?

Anonymous

Anonymous Tue 28 Jan 2020 00:14:59 No.11337667 Report

Quoted By:

>>11337607
By guessing.

Anonymous

Anonymous Tue 28 Jan 2020 02:34:55 No.11337950 Report

Quoted By: >>11339927

>>11337012
>why yes, I just do a finite element method with the space generated by the constant function, how did you know?

Anonymous

Anonymous Tue 28 Jan 2020 16:33:01 No.11339253 Report

Quoted By:

>>11336894
The Laplace Transform is no the only special function used to solve ODE's and PDE's.

Anonymous

Anonymous Tue 28 Jan 2020 16:41:21 No.11339271 Report

Quoted By:

>>11336894
>Can any differential equation be solved by applying Laplace Transform
no

Anonymous

Anonymous Tue 28 Jan 2020 19:01:07 No.11339634 Report

Quoted By: >>11339824 >>11339873

>>11336894
only linear differential equations

Anonymous

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Anonymous Tue 28 Jan 2020 19:04:07 No.11339639 Report

Quoted By:

Anonymous

Anonymous Tue 28 Jan 2020 19:45:26 No.11339760 Report

Quoted By:

>>11337607
Copying and pasting it into Wolfram.

Anonymous

Anonymous Tue 28 Jan 2020 20:10:03 No.11339824 Report

Quoted By: >>11339873

>>11339634
>>11336894
And even then for nonhomogeneous equations, the solution may involve a nonelementary antiderivative such as y” + y = arctan(x), but yes, any linear ODE

Anonymous

Anonymous Tue 28 Jan 2020 20:18:07 No.11339844 Report

Quoted By:

>>11336894
Babby's first transform.

JK I think it's a neat trick even if it becomes ineffective as you go deeper into the subject.

Anonymous

Anonymous Tue 28 Jan 2020 20:30:29 No.11339873 Report

Quoted By:

>>11339634
>>11339824
brainlets

Anonymous

Anonymous Tue 28 Jan 2020 20:55:12 No.11339927 Report

Quoted By:

>>11337950
kek'd. But seriously though, it works quite well with the appropriate function space.

Anonymous

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Anonymous Tue 28 Jan 2020 23:38:04 No.11340401 Report

Quoted By: >>11340419

>>11336954
Got a link to the paper? I'm a sucker for computational physics / maths. Is it used in graphics processing at all?

Anonymous

Anonymous Tue 28 Jan 2020 23:45:45 No.11340419 Report

Quoted By: >>11340482

>>11340401
Do you need to solve odes in graphics processing?

Anonymous

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Anonymous Wed 29 Jan 2020 00:00:11 No.11340482 Report

Quoted By: >>11340558

>>11340419
>odes in graphics processing?
Navier-Stokes and variants for fluid mechanics though that's PDE. Was curious if the method in questions is used as well as Finite Element.

Anonymous

Anonymous Wed 29 Jan 2020 00:25:56 No.11340558 Report

Quoted By:

>>11340482
Dormand-Prince methods are for odes, but I guess they might work well for pdes if you convert them into odes, never tried myself.

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