To update it or just to rewrite if it is unstable.

You can write SW/Firmware for anything---IF you have all the interface specs. I would doubt that any cellphone manufacturer would give this to you.

When you say "...rewrite...in Linux", do you mean that you want to create an OS for the cellphone that is based on Linux?

To modify the existing SW, you would need the source code

No.
For example I downloaded some firmware for my cell phone. Let's say it has v1.3. My cell phone has this firmware v1.3 but it's corrupted for some reason (the firmware). Now I wanna fix this and rewrite downloaded firmware to my cell phone so it will have correct one.

In Windows we normally have software from company that makes those devices. And we use those programs to rewrite firmware of cell phones. So is there any method I can use to rewrite firmwares in Linux? Download firmwares from Internet and upload it to cell phone.

P. S. And what is "SW"?

SW=Software

As I said, to modify the firmware, you will need the source code. Your statment about Windows implies that someone is supplying the source code---or simply the interface spec.

Perhaps you can give a specific example of a cell phone model and what they are supplying for programming,

I think the confusion stirs from the OP's understanding of "rewrite the firmware". He doesn't mean modifying the source, he simply means replacing his cellphone's firmware with a newer version (or similar). His phone and computer probably "physically" talk via a cable of some sort and he can make use of a piece of software (provided by the cellphone's manufacturer) in order to "logically" talk to the cellphone. Since these pieces of software are usually proprietary in nature, they also tend to only run on Windows machines.

posixculprit, you got me right. So I can't replace the firmware if I don't have Windows? No alternative for those programs from manufacturers?

I suppose the first step would be to check if the cellphone's producer doesn't provide software for Linux or technical documentation on how to communicate with the cellphone by means of a computer. In the likely event that they don't, you can give Wine (or the like) a try. If that fails, you can try disassembling the official software and try to figure out how it works (or use whatever other method to find this out) and then write your own, Linux-friendly, program.