       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:= 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

Send instant messages to your online friends http://uk.messenger.yahoo.com

```

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