You've described numerical integration as a linear sum. (wattsupwiththat.com)
Recent numerical integrations, however, suggest that stable planetary orbits exist: within three AUs (four AUs for retrograde orbits) of either Alpha Centauri A or B in the plane of the binary's orbit; only as far as 0.23 AU for 90 - degree inclined orbits; and beyond 70 AUs for planets circling both stars (Weigert and Holman, 1997). (solstation.com)
We find that virtually all candidate systems are stable, as tested by numerical integrations that assume a nominal mass - radius relationship. (arxiv.org)