Continue to Site

Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

calculating coficients of non-fourier series

Status
Not open for further replies.

mhamini

Member level 1
Joined
Aug 23, 2005
Messages
40
Helped
0
Reputation
0
Reaction score
0
Trophy points
1,286
Location
Iran-Tehran
Activity points
1,690
Hi

By solving this problem :

Θtt = a²Θxx ; (0<x<L , t>0)
Θ(x,0) = f(x);
Θt(x,0) = 0;
Θx(0,t) + αΘ(0,t) = 0;
Θx(L,t) + αΘ(L,t) = 0;
α is a positive constant;

I have this non-fourier serie now :

Θ(x,0) = ∑(AnCn)e^(αx)+(AnDn)e^(-αx) = f(x)

How can i obtain AnBn & AnDn cofficients?
 

(1) The first boundary condition is not correctly set
Θx(0,t) + αΘ(0,t) = 0
It should be
Θx(0,t) +bΘ(0,t) = 0
where b is NONPOSITIVE. This is very important, or you may end up with more than one solution.

(2) By separation of variables, when you set
Θ(x,t)=X(x)T(t)
you will have two equations:
T''(t)+λ a²T(t)=0
and
X''(x)+λX(x)=0
X'(0) + bX(0) = 0
X'(L) + cX(L) = 0
where b<0 and c>0
Try to solve this eigenvalue problem. You'll see that you have to deal with some transcendental equations to get the eigenvalues. The eigenfunctions are all combinations of sin and cos. You won't have exponential functions.
 

Status
Not open for further replies.

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Back
Top