An adaptive numerical integration code for a chain of transputers

Abstract

We consider the calculation of ∫ a bƒ(x) dx , on a linear chain of transputers of arbitrary length, in which each transputer calculates an approximation to this integral on a subinterval of equal length using an adaptive method based on the ten point Gaussain rule and the twenty-one point Kronrod extension. Extensive numerical testing on a chain of 32 T800s shows that if a large number of function evaluations are needed then linear speed-ups are achievable with any number of transputers.