ABSTRACT
The order of the approximation of P~(x) is the same as the order of the highest-order difference included in the evaluation. The first term in Eq. (5.32) is 1110, so evaluating that term gives an O(h) result. The second term in Eq. (5.32) is 11%, so evaluating that term yields an 0(h2 ) result, etc. Evaluating Eq. (5.32) term by term yields
P;,(3.5) = -0.07936_ = -0.08150_ = -0.08161
first order second order third order
Error = 0.00227 = 0.00013 = 0.00002
The first-order result is quite inaccurate. The second-and third-order results are quite good. In all cases, only five significant digits after the decimal place are obtained.
