RE: using FindRoot to find multiple answers in a domain?

• To: mathgroup at smc.vnet.net
• Subject: [mg69108] RE: [mg69059] using FindRoot to find multiple answers in a domain?
• From: "David Park" <djmp at earthlink.net>
• Date: Wed, 30 Aug 2006 06:33:18 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Akil,

Although it works only on 1D cases, in those cases it is much better and
more convenient than FindRoot.

Needs["Ersek`RootSearch`"]

RootSearch[Cos[antwoord] == Sin[antwoord], {antwoord, 0,  10Pi}]

{{antwoord -> 0.785398}, {antwoord -> 3.92699}, {antwoord ->
7.06858}, {antwoord -> 10.2102}, {antwoord -> 13.3518}, {antwoord ->
16.4934}, {antwoord -> 19.635}, {antwoord -> 22.7765}, {antwoord ->
25.9181}, {antwoord -> 29.0597}}

David Park

To: mathgroup at smc.vnet.net

I want to find all answers that exist in a certain domain, but FindRoot
gives only the first answer it finds (Using other methods like Solve,Reduce
etc takes too long, so Im stuck with using FindRoot). I give the problem I
have by example, the functions I use are really complex, but by solving the
problem for the example, I could solve t for the complex part.

Example:

Finding all intersections of Cos[x] and Sin[x] in the domain [0,10Pi]

Doing:
FindRoot[Cos[antwoord] == Sin[antwoord], {antwoord, 0, 0, 10Pi}]

FindRoot[Cos[antwoord] == Sin[antwoord], {antwoord, %, %, 10Pi}]

does not work the second FindRoot gives the exact same answer back. So using
this in a loop to find all intersections does not work.

Doing FindRoot[Cos[antwoord] == Sin[antwoord], {antwoord, %+0.01, %+0.01,
10Pi}] instead, also does not work.

Any way to find all intersections in a specified domain?

Akil

```

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