Controlling the solution of the Cauchy problem on a multiprocessor computer (Q1110280)

The paper is devoted to solving ordinary differential equations on multiprocessor computing systems. A method of solving the Cauchy problem with prespecified accuracy in minimum time is proposed. It is based on a modified predictor-corrector method intended to simplify the adjustment, at some points, of the parameter value (cf. number of points m). Moreover, in order to improve the estimate of the number of iterations for particular m and n (step size), a new error function is proposed. A procedure is described how to choose quasioptimal values of parameters for controlling the solution. The proposed method can be easily extended to other iterative procedures, in particular to Newton's method.