• Support PF! Buy your school textbooks, materials and every day products Here!

I am solving a PDE

  • Thread starter jahandideh
  • Start date
  • #1

Homework Statement



oh! after trying to re-solve a PDE I reached this:


Homework Equations


[tex]\sum\frac{4}{((2n-1)\pi)^2} (a+\frac{4(-1)^{n+1}}{(2n-1)\pi}) cos(\frac{2n-1}{2}\pi x) [/tex]

n goes feom 1 to [tex]\infty[/tex] and "a" is a constant value.

The Attempt at a Solution


the solution i am trying to reach is:

[tex]=\frac{1}{2} (1-x^{2}+(1-x)a)[/tex]

but i don't know how?
can anyone help please?
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,770
911
What is the Fourier series for [tex]\frac{1}{2} (1-x^{2}+(1-x)a)[/tex]?
 
  • #3
thanx for suggestion my buddy.
u know the orginal problem is a heat equation - one dimentional and time dependent-

[tex]T_{xx}+j^{2}=T_{t}[/tex]
[tex]T_{t}=-1/2j\frac{b}{cL}[/tex]
[tex]T(1,t)=0[/tex]
[tex]T(x,0)=0[/tex]

j,c,b are constant and 0[tex]\leq[/tex]x[tex]\leq[/tex]1

i solved the problem to here:

[tex] T(x,t)= j^{2} \sum (\frac{1}{\lambda_{n}^{2}}) \times \frac{b}{cL}+ \frac {2 \times -1^{n+1}}{\lambda_{n} cos(\lambda_{n}x + j^{2} \sum \frac{-1}{(\lambda_{n})^{2}}(e)^{-\lambda_{n}t} \left[\frac{b}{cL}+ \frac {2\times -1^{n+1}}{\lambda_{n}\right] cos(\lambda_{n}x)[/tex]
 

Related Threads for: I am solving a PDE

  • Last Post
Replies
2
Views
588
  • Last Post
Replies
1
Views
770
  • Last Post
Replies
4
Views
931
  • Last Post
Replies
2
Views
489
  • Last Post
Replies
0
Views
1K
Replies
2
Views
994
  • Last Post
Replies
4
Views
757
  • Last Post
Replies
4
Views
585
Top