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symbolic derivatives

  • To: mathgroup at (mathgroup mathgroup)
  • Subject: [mg320] symbolic derivatives
  • From: Edward Birchfield <edward at>
  • Date: Mon, 12 Dec 1994 13:47:19 CST

Dear Mathgroup members,

I am trying to utilize FindRoot to solve a system of nonlinear algebraic
equations.  Involved in these equations are some very simple conditional
functions.  For example:

mi1[ts1_,vice_] :=  0.                    /;  ts1 <  tscrit || vice <= 0.
mi1[ts1_,vice_] :=  gammats1 (ts1-tscrit)(1 - Exp[mlam (ts1-tscrit)]  /;  
                    ts1 >= tscrit && vice >  0.
where gammts1, mlam  and tscrit are constants.

Although these functions are continuous, FindRoot gives an error message to the
effect that the Jacobian matrix (needed for Newton's method), cannot be
symbollically determined; it also suggests trying with 2 initial guesses instead
of one (so the secant method can be utilized).  I conclude that Mathematica
cannot differentiate continuously differentiable functions which are subject to

I prefer to use Newton's method if possible.  Does anyone know of a package that
will solve nonlinear algebraic equations? Ideally such a package should allow 
one to provide the Jacobian matrix oneself.

Edward Birchfield

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