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$\frac{d^2 \theta}{dx^2} (1 + \beta \theta) + \beta \left(\frac{d \theta}{d x}\right)^2 - m^2 \theta = 0$

Boundary Conditions $\theta=100$ at $x = 0$, $\frac{d\theta}{dx} = 0$ at $x = 2$

$\beta$ and $m$ are constants. Please help me solve this numerically (using finite difference). The squared term is really complicating things! Thank You!

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    What have you tried already? Also, is this a homework question? If yes, please state this.2012-03-15
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    av tried alot actually... infact i solved analytically to a considerable stage but solving numerically has been a challenge.2012-03-15
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    av tried alot actually d latest being nonlinear FDE approach using iteration(lagging)... but the squared term is given me a problem. Also is d differential boundary condition2012-03-15
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    It also helps to post this question on http://physics.stackexchange.com/2012-03-15
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    thks Kirthi...jus did that!2012-03-15
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    Or post at http://scicomp.stackexchange.com2012-03-15
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    Can you explain more in detail what the difficulty is? If you set $\theta_i' = \frac{\theta_{i+1}-\theta_{i-1}}{2 h}$ and $\theta_i'' = \frac{\theta_{i+1}-2\theta_{i}+\theta{i-1}}{h^2}$ then you have an algebraic expression to deal with.2012-03-15

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