Research Article

New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time Integration

Table 1

Closed Newton-Cotes integral rules.


0 1 1
1 1/2 1 1
2 1/3 1 4 1
3 3/8 1 3 3 1
4 2/45 7 32 12 32 7
5 5/288 19 75 50 50 75 19
6 1/140 41216 27272 27216 41
77/17280751357713232989 298913233577 751
84/141759895888−92810496−454010496−9285888989