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MathGroup Archive 2007

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Re: Solving Nonlinear Equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80545] Re: Solving Nonlinear Equations
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sun, 26 Aug 2007 02:54:58 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fals2t$g7g$1@smc.vnet.net>

Biyana, D. (Dugmore) wrote:

> I'm using Mathematica V6.0.1 and I have a system of 4 nonlinear equations
> which I'm trying to solve using FindRoot:
>  
> FindRoot[{m1==C-D*Exp[1/(2*B^2)]*Sinh[A/B],
>  
> m2==C^2+(D^2/2)(Exp[2/B^2]Cosh[2A/B]-1)-2C*D*Exp[1/(2B^2)]*Sinh[A/B],
>  
> m3==C^3-3*C^3*D*Exp[1/(2B^2)]*Sinh[A/B],+3*C(D^2/2))*(Exp[2/B^2]Cosh[2A/B]-1
> )+(D^3/4)(3*Exp[1/(2B^2)]Sinh[A/B]-Exp[9/(2B^2)]Sinh[3A/B]),
>  
> m4==C^4-4(C^3)D*Exp[1/(2B^2)]*Sinh[A/B]+3(C*D)^2))*(Exp[2/B^2]Cosh[2A/B]-1)+
> (D^3/4)+C*D^3(3*Exp[1/(2B^2)]Sinh[A/B]-Exp[9/(2B^2)]Sinh[3A/B])+(D^4/8)(Exp[
> 8/(B^2)]*Cosh
> [4A/B]-4*Exp[2/(B^2)]Cosh[2A/B]),{{A,initA},{B,initB},{C,initC},{D,initD}}]
>  
> I get the message " FindRoot::cvmit : Failed to converge to the requested
> accuracy..." which I suspect is a result of initial values of A, B,C, and D.
> What trick can one use to get accepatble initial values?

First, note that the expression you posted contains several syntax 
errors (missing parentheses, curly bracket, comma in the middle of an 
equation, possibly many others but I gave up trying to fix it in a 
meaningful way).

Second, though the initial values may influence the results (and the 
method used by FindRoot), it might be interesting to adjust some of the 
internal parameters such as AccuracyGoal, MaxIterations, PrecisionGoal, 
WorkingPrecision, to name a few.

-- 
Jean-Marc


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