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MathGroup Archive 2007

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Recursive FindRoot with initial values as a list

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77023] Recursive FindRoot with initial values as a list
  • From: "R.G" <gobiithasan at yahoo.com.my>
  • Date: Thu, 31 May 2007 05:32:58 -0400 (EDT)

Greetings...
Say I have a function defined as:
f[a_, b_]:= Integrate[Sin[x] + 3, {x, a, b}]

I can find b with given f[a,b]=2 and initial value=0:
In[1]:= Initialvalue = 0;
     s1 = FindRoot[f[0, unknown] == 2, {unknown,Initialvalue}];
     x1 = s1[[ 1, 2]]

Now, using the x1 value obtained from FindRoot, I can find x2:
     s2 = FindRoot[f[x1, unknown] == 2, {unknown,Initialvalue}];
     x2 = s2[[ 1, 2]]

If I have initialvalue in a list form:
InitialValues={initialvalue1,initialvalue2,...,initialvalueN} 

in which each si should get InitialValues[[i]], in general form:

\!\(s\_i = 
    FindRoot[{f[x\_\(i - 1\), unknown] \[Equal] 2}, {unknown, 
        InitialValues[\([i]\)]}]\)

where

\!\(x\_i = s\_i[\([1, 2]\)]\)

How do I code it in Mathematica please? Thanking in advance...

~R.G


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