CFD theoretical discretization exercise -- CFD Online Discussion Forums

July 9, 2016, 08:18	CFD theoretical discretization exercise	#1
maciekao New Member Maciek Join Date: Jul 2016 Posts: 1 Rep Power: 0	Hi all. I have CFD exercise to solve. Prove that $\frac{ \partial u}{ \partial x}\|_i = \frac{u_{i-2} - 2u_{i-1} + u_i}{h^2}$ using $\frac{ \partial^2u}{ \partial x^2 }= \alpha u_{i-2} + \beta u_{i-1} + \gamma u_i$ $u_{i-2} = u(x-2h)$ $u_{i-1} = u(x-h)$ I know that I have to apply Taylor's series, and use the coefficent method. Unfortunattely, there is a small problem-I have to prove the first derivative, but at the end I find the second derivative. I would appreciate some tips

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