Algorithm 502: Dependence of Solution of Nonlinear Systems on a Parameter [C5]

DESCRIPTION The Fortran algorithm DERPAR is a subroutine suitable for evaluation of the dependence of the solution x~,..., xn of a system of equations on the parameter a. The modified method of David~nko [-1, 2, 33, which applies the implicit function theorem, is used in combination with the Newton method and Adams integration formulas. A similar procedure was used by Deist and Sefor ['43, who made use of an introduced parameter. To establish the dependence x (a), the following set of differential equations can be derived: dx = _r_i(x ' a) of__ x(ao) = Xo. (2) da Oa' Here T ' 0a ''" '0al' If r (x (a), ~) is a regular matrix for (~0, al), then x (a) obtained by integration of (2) satisfies f(x(a),~) = O, a E (ao, a,). but not for profit, all or part of this material is granted provided that ACM's copyright notice is given and that reference is made to the publication, to its date of issue, and to the fact that reprinting privileges were granted by permission of the Association for Computing Machinery.