98 Ordinary Differential Equations/Approximate solution
Slopefn-m+1-....._. ~- Slope[,
X ' n-pI' (xn-m+11Yn-m+1) ''\/...
Slope fn-m / "
;yc,,_.,y,_,,) \Interpolating polynomial p(x)L
j ""•'------Interval of interpolation----'>1>-11
j ..... ,..____Interval of integration --->1>-11
F igure 2.13 Mult istep Integration Diagram for r = n
Choosing r = n, p = 0, and q = 1 results in a set of formulas which are
known as Adams-Bashforth formulas. Determining t he interpolating p oly-
nomial for the first few values of m and integrating results in the foll owing
formulas and t heir local discretization errors.