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To show that a scheme is consistent we define a smooth function $\phi$, and consider the following:

$$\frac{\phi_m^{n+1}-\phi_m^{n-1}}{2k}+a\left(\frac{\phi_{m+1}^{n}-\phi_{m-1}^{n}}{2h}\right)=0$$

I'm stuck on showing how to demonstrate this. I understand that we use Taylor series, then we find the difference between $\phi u-\phi_{k,h}=0$ as $(h,k)\to 0$.

emka
  • 6,494
  • Just expand each grid function using taylor expansion. Looks like it's (2,2) accurate so you don't need many terms in each expansion. – sjf2468 Nov 02 '16 at 22:45

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