- #1

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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)

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- #1

- 3

- 0

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)

- #2

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Exactly how are you applying "finite difference"? Are you assuming a linear solution overe each interval?

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- #3

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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..

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..

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- #4

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thanks for your attention

- #5

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Have you decided upon a strategy to take care of the non-linearity?

- #6

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yes Newton method

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