Dynamic Schema

I have very dynamic data that i want to write to an avro file. The solution
i have is to store all that data in the memory and then calculate the
schema, and then start the writing.

This causes the files to be smaller in size, because of the memory
limitations.

What i am looking for is that i will start data as and when it is
collected, but how should i compute the schema in this case? Can i change
the schema for an avro file?

Thanks
Amit