This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
Applets run on the client in a browser where as servlets run on the server. Except the "lets" part, they have nothing in common.
As far as I can understand your question, your applet currently computes some data and you want to move this computation to the server using servlets.
You can always move the computing blocks (methods) to the server and invoke them from the applet. How to invoke them would depend on your architecture. RMI or Object I/O over HTTP are two options which immediately come to mind.
You might find this link useful
http://faq.javaranch.com/java/AppletsFaq#servlet Also keep in mind that "applets can only dial home", meaning they can only communicate back to the server from which they originated.
I see Bear has already informed you about changing the post title. It is expected that you do so before posting again.