Compilation problem in Java program to find the largest value in an array

You may just iterate the array of numbers and keep track of the largest value seen:

int largest = Integer.MIN_VALUE;

for (int j=0; j < array.length; j++) {
    if (array[j] > largest) {
        largest = array[j];
    }
}

Note: The above snippet assumes that you have at least one number in the input array.

1. You can use IntStream.max() method to find the maximum element of a stream of int primitives:

   int[] arr = {4, 7, 5, 3, 2, 9, 2, 7, 6, 7};
   
   int max = Arrays.stream(arr).max().getAsInt();
   
   System.out.println(max); // 9
   

2. You can use Stream.max(Comparator) method to find the maximum element of a stream of Integer objects:

   List<Integer> list =
           Arrays.asList(6, 10, 2, 1, 6, 4, 5, 8, 9, 8);
   
   Integer max2 = list.stream()
           .max(Comparator.comparingInt(Integer::intValue))
           .get();
   
   System.out.println(max2); // 10
   

^{See also:
• How to find first 5 highest value in a two dimensional array?
• Selection sort of array in Java}

As said above, pay attention to the variables scope:

public class Test {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        System.out.println("Enter a list of integers: ");

        int array[] = new int[10];
        for (int i = 0; i < array.length; i++) {
            array[i] = s.nextInt();
        }

        int maximum = 0;
        for (int j = 0; j < array.length - 1; j++) {
            maximum = Math.max(array[j], array[j + 1]);
        }

        System.out.println("Largest number of the list: " + maximum);
    }
}

You're defining your maximum variable inside the for loop block, making it a local variable, then you're trying to access the value on this variable outside of its definition block, that is why Java cannot find such variable, because it does not exist on that scope. Try This:

public class Test {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        System.out.println("Enter a list of integers: ");
        int array[] = new int[10];
        int maximum = 0;
        for (int i = 0; i < array.length; i++) {
            array[i] = s.nextInt();
        }

        for (int j = 0; j < array.length; j++) {
            if (j < array.length) {
                maximum = Math.max(array[j], array[j + 1]);
            }
        }

        System.out.println("Largest number of the list: " + maximum);
    }
}

Try reading this link for a further explanation on scopes and variables.