CalculateAreaEllipse()

Step 1: Understand the Math for Elliptical Area Calculation

The first step is to understand the mathematics behind the area calculation of an ellipse. The formula to calculate the area of an ellipse is π * a * b where a and b are the semi-major and semi-minor axis lengths respectively.

Step 2: Define the Function

We'll define a function in Java that takes the lengths of two axes as parameters, performs the calculation and returns the result. Here's what the function signature would look like:

public static double calculateAreaEllipse(double a, double b) 

Step 3: Implement the Calculation

In this function, we'll invoke Math.PI, a constant in the Java Math class that represents the mathematical value of π, and multiply it with our parameters a and b then return the result.

public static double calculateAreaEllipse(double a, double b) {
    return Math.PI * a * b;
}

Step 4: Handle Possible Errors

We should account for potential errors. There are few ways we could go about this, the simplest is to absolve negative values before performing the calculation.

public static double calculateAreaEllipse(double a, double b) {
    a = Math.abs(a);
    b = Math.abs(b);
    return Math.PI * a * b;
}

Step 5: Test the Function

Finally, test the function with some values to ensure it's working as expected.

public static void main(String[] args) {
    System.out.println(calculateAreaEllipse(5, 2));
}

In conclusion, we have now successfully implemented a function in Java to calculate the area of an ellipse.