Question

How to find a solution for the heat equation that satisfies the Boundary Conditions and the Initial Condition.

Answer 1

@satellite73 @Miracrown

Answer 2

and no we can't have two separate equations because that won't equal...though I would love to do that because that would make my life easier.

Answer 3

this is really a find the almighty magic equation that can satisfy the heat equation...meaning u_t=u_xx(k)

Answer 4

though we need one, not two separate ones...meaning I can't have u(x,t) = t+x^2-1 and then take 2 antiderivatives of x and then do u_xx... that's two different equations that don't equal

Answer 5

@inkyvoyd Fourier as in Fourier Series or Fourier Transform?

Answer 6

I don't think Fourier Series will help for heat equations -_-

Answer 7

@satellite73 help ussssss

Answer 8

@Hero @Callisto ??

Answer 9

I know...@agent0smith can help us because he's so smart

Answer 10

@agent0smith help us lol

Answer 11

@zzr0ck3r

Answer 12

yuk sorry, I suck at this stuff

Answer 13

What does IC stand for?

Answer 14

@FibonacciChick666 Initial COndition

Answer 15

BV is base volume then?

Answer 16

Hey I'm grubby green!!!!!

Answer 17

no Boundary Value.

Answer 18

D.E Differential Equation
B.C/B.V = Boundary Condition. Boundary Value
I.C - Initital COndition... I need to find an equation a unique one to satisfy the heat equation.

Answer 19

ok hmm. Well let me see, first is this for ODE or physics?

Answer 20

Partial differential equations.

Answer 21

ok, I can try, no guarantees.(Don't actually have that class) I would start with finding the \(u_{xx}\) term by using the last IC section

Answer 22

and by tagging someone better than me at this @SithsAndGiggles, have you had pde?

Answer 23

Nope, not yet I'm afraid :(

Answer 24

@FibonacciChick666 I can't have two separate equations... meaning I can't have a u(x,t) = t+x^2+1 and take the derivative.... can't have u(x,t) = x^4/12+1/2x^2 either

Answer 25

doesn't work that way because I've tried it on a wave equation... the u_xx wasn't equal to the v_tt

Answer 26

ok so let's try logic if u(0,t)=0 and u(x,0)=x^2-1, then we must have t=1

Answer 27

right?

Answer 28

hmm how would t = 1? unless that's from the other Boundary Condition.

Answer 29

hmm wait a sec.. we need to find an equation that can satisfy the B.C meaning if x = 0, 1, the end result should be 0 on both B,C.s

Answer 30

sorry, I mean that the t section of the eq must just be a constant and sinceu(x,0)=x^2-1 the t must be something like c=1 to negate the -1 from before. But that doesn't make sense...

Answer 31

when I did this similar problem with the wave equation earlier.. I took separate cases... like find an equation that satisfies the t portion of the wave equation the same goes for x and that went well until my professor pointed out that it has to be one equation, not two different ones. so I was peeved at that

Answer 32

ok so paul has an outline for PDE might help http://tutorial.math.lamar.edu/Classes/DE/TheHeatEquation.aspx

Answer 33

that doesn't help ..

Answer 34

the heat eq section doesn't?

Answer 35

no I am not solving anything... I am finding the perfect solution for this..

Answer 36

it didn't say to solve using duhamel's principle...

Answer 37

how about this one? I'm trying to see if we can relate this set up to something http://tutorial.math.lamar.edu/Classes/DE/SolvingHeatEquation.aspx

Answer 38

you may not want to solve, but that will yeild a general equation

Answer 39

yeah....I'm starting to think that might work.. I have done separation of variables before f

Answer 40

like if I let f(x) = x^2+1 and 1 = L I can just go backwards on it.

Answer 41

I think, it is a very similar problem to the one you posed. As i have not nor ever(unfortunately) taken PDE, I can only show you my work with no real knowledge just 1st opinion.

Answer 42

don't take it.. my homework assignments were at least 20 pages.

Answer 43

I'm doing ODE 2 instead, Ilike ode, it's easy for me. and hw depends on the teacher,i won't take it without Rabier. He is like the best most clear teacher ever. Very very rigorous grader though

Answer 44

you may like this too http://freevideolectures.com/Course/3294/Partial-differential-equations

Answer 45

use that link and start at lesson 25!!!!^^^^

Answer 46

here!! http://freevideolectures.com/Course/3294/Partial-differential-equations/25

Answer 47

@dan815 these wave equations...

Answer 48

#4 is using D'Alemberts and 5 is using harmonic solutions right? @dan815

Answer 49

I am hoping that 0 <x<oo is a typo because D'Alemberts is -oo<x<oo and that equations fits perfectly with that defintion.

Answer 50

@ganeshie8

Answer 51

@dan815 you have done wave equations right? now tell me if #4 is a clear D'Alemberts and 5 is harmonic product solutions being used in here?

Answer 52

i dunno i ust solve it

Answer 53

the last conidtion apply last, maybe write in fourier series too

Answer 54

show me what u got so far

Answer 55

damn I have to scan it first..

Answer 56

which problem are you talking about for the last condition? 4 or 5?

Answer 57

https://www.writelatex.com/1997791ptmsbb#/5032584/ look at section 5.3 #6 that is similar to #5 on that sheet.

Answer 58

Section 5.2 1b 1f is similar to #4

Answer 59

@dan815

Answer 60

yay! @Alchemista is here again ^_^

Answer 61

ok wait a sec... I don't remember using Fouriers for waves, so that shiz isn't going to work.

Answer 62

ok so u said for one of them u have to use d'alembert?

Answer 63

u(x,t)=F(x-ct)+G(x+ct)

Answer 64

rewrite i that form first

Answer 65

I know what D'Alemberts is.......from that other file we only have a g(x) so only the g(x) is being used @dan815

Answer 66

http://assets.openstudy.com/updates/attachments/548ba787e4b05733b80cd8ef-usukidoll-1418536150509-waveequations.png

#4 is Dalemberts and since we only have g(x) only the g(r) dr portion is being used.. then take antiderivative...integrate..blah blah it's there ^_^

Answer 67

oh u shud look at how wave eqn is derived then, wave eqn has symmetry about a speed its traveling