Abstract: A self starting predictor corrector method of arbitrary order is disclosed that uses exact stability integration in network designs for application in systems optimizing control of aircraft through improved numerical techniques. Such method defines a self starting predictor corrector routine for a numerical solution of differential equations having a main process that computes derivatives of the states with a n-th order numerical solution for a n-th order differential equation. Moreover, such method configures an exact stability algorithm for generating a numerical integration of a high order of any type linear or nonlinear filter or network by constraining extraneous eigenvalues in the high order filter or network to be a definite value.