Linear multistep method: Difference between revisions

Revision as of 15:03, 26 March 2015

Revision as of 20:37, 28 March 2015

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\end{align} </math>

The derivation of the Adams–Moulton methods is similar to that of the Adams–Bashforth method; however, the interpolating polynomial uses not only the points <math> t_{n−1n-1},\dots, t_{n-s} </math>, as above, but also <math> t_n </math>. The coefficients are given by

:<math> b_{s-j} = \frac{(-1)^j}{j!(s-j)!} \int_0^1 \prod_{i=0 \atop i\ne j}^{s} (u+i-1) \,du, \qquad \text{for } j=0,\ldots,s. </math>