Richardson Extrapolation

blackthunder

New member
Hey, I was hoping someone could help me with this question I can't get at all.

If $$\phi{h}=L-c_1h^{\frac{1}{2}}-c_2h^{\frac{2}{2}}-c_3h^{\frac{3}{2}}-...$$ , then what combination of $$\phi{h}$$ and $$\phi(\frac{h}{2})$$ should give a more accurate estimate of L.

Thanks for any help.

CaptainBlack

Well-known member
Hey, I was hoping someone could help me with this question I can't get at all.

If $$\phi{h}=L-c_1h^{\frac{1}{2}}-c_2h^{\frac{2}{2}}-c_3h^{\frac{3}{2}}-...$$ , then what combination of $$\phi{h}$$ and $$\phi(\frac{h}{2})$$ should give a more accurate estimate of L.

Thanks for any help.
Assuming that the $$c_i$$s are unknown we can write:

$\phi( h)=L-c_1h^{1/2}+O( h)$

and $$n=1/2$$ in the Richardson extrapolation formula and so the Richardson extrapolation for $$L$$ is:

$R_L=\frac{2^{1/2}\phi(h/2)-\phi( h)}{2^{1/2}-1}$

CB