Richardson's method applied to an O(h) method
Forward difference quotient for y = e^x, with h = 0.1
i O(h) O(h^2) O(h^3) O(h^4) O(h^5)
h 2.85884195487388
h/2 2.78738579208238 2.71592962929087
h/4 2.75254528427222 2.71770477646207 2.71829649218581
h/8 2.73534210024472 2.71813891621722 2.71828362946894 2.71828179193796
h/16 2.72679418400678 2.71824626776883 2.71828205161937 2.71828182621229 2.71828182849725
Richardson's method applied to an O(h^2) method
Balanced difference quotient for y = e^x, with h = 0.1
i O(h^2) O(h^4) O(h^6) O(h^8) O(h^10)
h 2.72281456394742
h/2 2.71941458747318 2.71828126198177
h/4 2.71856499166488 2.71828179306212 2.71828182846747
h/8 2.71835261760135 2.71828182624684 2.71828182845915 2.71828182845902
h/16 2.71829952564097 2.71828182832085 2.71828182845912 2.71828182845911 2.71828182845912
e = 2.71828182845905