       Re: Recursive FindRoot with initial values as a list

• To: mathgroup at smc.vnet.net
• Subject: [mg77047] Re: Recursive FindRoot with initial values as a list
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Fri, 1 Jun 2007 02:48:59 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <f3m4qv\$fgl\$1@smc.vnet.net>

```R.G wrote:
> 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

Hi,

One possible way of doing what you are looking for is the use a
functional construct such as NestList and a pure function (that why you
can see #1 and &). For instance,

In:= f[a_, b_] = Integrate[Sin[x] + 3, {x, a, b}];
With[{Initialvalue = 0, n = 5},
Rest[NestList[FindRoot[f[#1, unknown] == 2,
{unknown, Initialvalue}][[1, 2]] & , 0, n]]]

Out= {0.607102, 1.13938, 1.64271, 2.15069, 2.69881}

Cheers,
Jean-Marc

```

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