| | | | | | | | | |
| 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 | | | | | | | | |