Calculus/Matrix Q: finite diff. matrix for d^2(x)/dx^2 + u =
- Thread starter Goistein
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D
Deleted member 4993
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Re: Calculus/Matrix Question
What type of difference equation you are supposed to write - forward, backward or central?
Please show us your work - if you want us to correct your mistake?
Goistein said:
What type of difference equation you are supposed to write - forward, backward or central?
Please show us your work - if you want us to correct your mistake?
Re: Calculus/Matrix Question
I looked at an example and it looked like the solution for d^2(u)/dx^2= f(x) 0<x<1 was
[2 -1 0 0 0
-1 2 -1 0 0
0 -1 2 -1 0
0 0 -1 2 -1
0 0 0 -1 2]
So since it asked for a 3x3 matrix, I figured it was
[2 -1 0
-1 2 -1
0 -1 2]
p.s. They also gave me h=1/4 if that helps, but if it doesn't I think in the solution they use forward elimination.
I looked at an example and it looked like the solution for d^2(u)/dx^2= f(x) 0<x<1 was
[2 -1 0 0 0
-1 2 -1 0 0
0 -1 2 -1 0
0 0 -1 2 -1
0 0 0 -1 2]
So since it asked for a 3x3 matrix, I figured it was
[2 -1 0
-1 2 -1
0 -1 2]
p.s. They also gave me h=1/4 if that helps, but if it doesn't I think in the solution they use forward elimination.
D
Deleted member 4993
Guest
Re: Calculus/Matrix Question
First write the difference equation of the given ODE - the matrix would simply fall-out of there after you apply the boundary conditions.
Show us the difference equation that you would write for the given ODE.
16 in the ODE comes from h^2 terms.
First write the difference equation of the given ODE - the matrix would simply fall-out of there after you apply the boundary conditions.
Show us the difference equation that you would write for the given ODE.
16 in the ODE comes from h^2 terms.
D
Deleted member 4993
Guest
Re: Calculus/Matrix Question
\(\displaystyle \frac{d^2u}{dx^2} \, = \, \frac{u_{n-1} \, - \, 2\cdot u_n\, + \, u_{n+1}}{h^2}\)
and continue from there....
Goistein said:
\(\displaystyle \frac{d^2u}{dx^2} \, = \, \frac{u_{n-1} \, - \, 2\cdot u_n\, + \, u_{n+1}}{h^2}\)
and continue from there....
