A parallel iterated correction algorithm for the numerical solution of Volterra equations Original Research Article

We present an algorithm by which the discrete numerical solution of a Volterra integral equation (with non-singular kernel) obtained from a classical Newton-Cotes-type approximation of its integral part is corrected in an iterative way. The correction mechanism, which is based upon the use of non-purely polynomial quadrature rules, turns out to be parallelizable. A parallel algorithm which is suited for a small number of processors is presented and has been implemented on a ring of transputers. Its efficiency is illustrated and analyzed by means of three test equations.