Possible To Check If Classes Contains A Specific Method And Then Run That Method?

I'm working on a simple 2D Game Framework. Currently it's creating a window, but I'm working on an update method.

I constantly export the framework as a .jar file, and I've added it to the game's build path (using eclipse). I wonder if I can check all classes in the game-project (the project in which I've refecrenced the Framework in) for a specific method (for example update()) and call all found methods with that name from the framework's main class, like this:

public class FrameworkClass1 {
  private void checkForUpdateMethods() {
// Check for update methods on program start
} public void update() {
runAllFoundUpdateMethods(); // Run all update methods found in the scan
}
}

I want to do this because it would be a simple way to update and render the game. If the main game-class look something like this:

public class Game {
public void update() {
// Update the game every time this is ran
}
}

it will be automatically updated, because it contains a method named update(), instead of naming the main game-class with a specific name etc. It will simply be more flexible that way!