Simpson's double integral won't work in java

Question

So I had to write an algorithm for the Simpson's double integral so I can find the answer in a much faster manner. I had a guide that showed the steps to follow to write this program. After following this guide and running it in netbeans, I found out that the values coming out of the program where not really close to the real answer. This is the code that I written in java:

  //INPUT
        double a = 0,b = 1; // Endpoints
        int m = 8,n = 4;

        double K1 = 0, K2 = 0, K3 = 0;

        //OUPUT 

        //Step 1
        double h = (b - a) / n;
        double j1 = 0; //End terms
        double j2 = 0; //Even terms
        double j3 = 0; //Odd terms

        //Step 2
        for(int i = 0; i <= n; i++){
            //Step 3
            double x = a + (i * h);

            double hX = (d(x) - c(x)) / m;
             K1 = f(x, c(x)) + f(x, d(x)); // End terms


             //Step 4
             for (int j = 1; j < (m-1); j++){
                 //Step 5
                 double y = c(x) + (j * hX);
                 double q = f(x,y);


                 //Step 6
                 if (j % 2 == 0){
                     K2 = K2 + q;
                 }
                 else
                     K3 = K3 + q;
             }

             //Step 7 
             double l = (K1 + (2*K2) + (4*K3)) * (hX / 3);

             //Step 8
             if (i == 0 || i == n)
                 j1 = j1 + l;
             else if (i % 2 == 0)
                 j2 = j2 + l;
             else
                 j3 = j3 + l;

        }

        double j = h * (j1 + (2 * j2) + (4 * j3)) / 3;
        System.out.println("j = " + j);

    }


    public static double c(double x){
        return x;
    }

    public static double d(double x){
        return 2 * x;
    }

    public static double f(double x, double y){
        return (Math.pow(y, 2) + Math.pow(x, 3));
    }

I tried debugging the program several times but I haven't yet found why I am encountering this mistake. If there's any mistake that you find in my code please let me know to see if it fixes it. For the given example, I am getting the value of 0.9069281684027777 instead of having the correct value which is 0.7838542. Thank you for your help. You can also see the guide that I followed to be able to create this program.

Answer 1

I did not check the math, the large error seems to indicate an error in the algorithm implemented. The for-bounds are dubious. And floating point errors exist.

Instead of multiplying a fraction by a running index (which would multiply the floating point approximation error in the fraction), better do:

Instead:

    double h = (b - a) / n;
    for (int i = 0; i <= n; i++) {
        double x = a + (i * h);

do

    for (int i = 0; i < n; i++) {
        double x = a + i * (b - a) / n;

or

    for (int i = 0; i <= n; i++) {
        double x = a + i * (b - a) / (n + 1);

The boundary n being a bit unclear to me.