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scaling routine USCAL. One has to use the function supply to store thefunction handle to USCAL and the scaling vectors in the structure array.For example, one writesuh = @myUsal;scalc = [...];scalr = [...];setup = supply(’uscal’, uh, ’scalc’, scalc, ...’scalr’, scalr);to supply these data.To indicate that automatic scaling is not used, setup.info(13) is set to1. The value of setup.iw(16) is set to 0 if one wants to disable anyscaling or setup.iw(16) is set to 2 if one wants to use ones own scalingfunction.NLSYSSOLVER In every step the BDF-method uses the simplified Gauss-Newton method to solve the nonlinear system. If µ=0, then one can letthe code decide when a new iteration-matrix is needed. The method usedfor this decision is the same as in DASSL [11]. One can also let the codeuse the classical Gauss-Newton method, which is much slower than thedefault method.To indicate that the simplified Gauss-Newton method is not used,setup.info(14) is set to 1. The value of setup.iw(2) is set to 0 if oneprefers the method used in DASSL or setup.iw(2) is set to 2 if one wantsthe code to use the classical Gauss-Newton method in every step.STARTINGVALUES In every step of the BDF-solver the code obtains thestarting values for X(1 : N) and XPRIME for the Gauss-Newton iterationsby interpolation. For the remaining starting values X(N+1 : (µ +2)N) ittakes by default X(N+1 : 2N)=XPRIME and classical homotopy for theremaining values, i.e. it takes the last solutions as starting values for thenext step.To indicate this changed method for obtaining starting values,setup.info(15) is set to 1. The value of setup.iw(17) is set to 0 if onewants to use classical homotopy also for X(N+1:2N), setup.iw(17) is setto 2 if one wants the code to compute the starting values for X(N+1:2N)by linear extrapolation, or setup.info(17) is set to 3 if one wants thecode to obtain all values X(N+1:(µ +2)N) by linear extrapolation.COND If the user does not know the characteristic values of the problem, therank decisions made to compute the characteristic values may suffer fromscaling problems and of the error made in every BDF-step. A singularvalue of a matrix is taken to be zero, if it is smaller than the largest singularvalue multiplied by COND −1 . By default, we set COND = 10 12 .24