Problem with finite diffence method

  • Thread starter zeynepkisa
  • Start date
  • #1
I have been trying to solve this problem for hours and hours but derivative boundary condition makes the it very hard. can anybody help me about nonlineer eq. solution with finite difference??

question is:

u'' + 3*u^2 *( 1 / (sin^2(x)) =2.5
BCs:

u'(1)=0.95
u(2)=0.83
h=0.25
(radian for sin function)
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,847
969
Exactly how are you applying "finite difference"? Are you assuming a linear solution overe each interval?
 
Last edited by a moderator:
  • #3
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
10,025
135
As for the boundary condition, since it involves a derivative, you should regard it the actual left boundary as an interior point.
Thus, introduce a fictitious boundary point [itex]x_{0}=1-h[/tex]
and you have n+1 points [itex]x_{0}, x_{1}=1,\cdots{x}_{n}=2[/tex]

The differential equation should be satisfied at all interior points, so that you have n+1 non-linear equations like this:
[tex]\frac{u_{2}-u_{0}}{2h}=0.95, u_{n}=0.83[/tex]
and:
[tex]\frac{u_{i+1}-2u_{i}+u_{i-1}}{h^{2}}+3u_{i}^{2}\frac{1}{\sin^{2}(x_{i})}=2.5, i=1,\cdots{n-1}[/tex]

Now, you are ready to see how to implement a loop structure to actually solve this system approximately..
 
Last edited:
  • #4
thanks for your attention
 
  • #5
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
10,025
135
Have you decided upon a strategy to take care of the non-linearity?
 
  • #6
yes newton method
 

Related Threads on Problem with finite diffence method

  • Last Post
Replies
6
Views
995
  • Last Post
Replies
1
Views
2K
Replies
2
Views
8K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
0
Views
1K
Replies
5
Views
876
Replies
1
Views
931
Replies
9
Views
2K
Replies
6
Views
1K
Replies
4
Views
973
Top