Cauchy

import java.util.ArrayList;

class EuilerSolve {

    private double a = 1.0;
    private double b = 5.0;
    //    private double V = 1;
    private double V = 3;
    private int N = 15;


    ArrayList<Double> xList = new ArrayList<>();
    ArrayList<Double> exactYList = new ArrayList<>();
    ArrayList<Double> euilerYList = new ArrayList<>();
    ArrayList<Double> diffList = new ArrayList<>();
    ArrayList<Double> yList = new ArrayList<>();

    double origF(double x) {
        return V * (x * x * x) + (x * x) + x;
    }

    double stepF(double x, double fx) {
        return V * (x * x * x) + (3 * V + 1) * (x * x) + 3 * x + 1 - fx;
    }

    public void calcImproved() {
        double step;
        step = (b - a) / (N - 1);
        xList.add(a);
        euilerYList.add(V + 2);

        for (int i = 1; i < N; i++) {
            xList.add(xList.get(i - 1) + step);
        }
        for (int i = 1; i < xList.size(); i++) {
            double _tmpX = (xList.get(i - 1) + xList.get(i)) / 2;
            double _tmpFx = euilerYList.get(i - 1) + (step / 2) * stepF(xList.get(i - 1), euilerYList.get(i - 1));

            double dy = euilerYList.get(i - 1) + step * stepF(_tmpX, _tmpFx);
            euilerYList.add(dy);
            //System.out.println(_tmpX);
        }
        for (int i = 0; i < N; i++) {
            double exactVal = origF(xList.get(i));
            exactYList.add(exactVal);
            diffList.add(Math.abs(exactVal - euilerYList.get(i)));
        }

        System.out.format("\tx\teuiler y\texact y\t\tdiff\n");
        for (int i = 0; i < N; i++) {
            System.out.format("%.3f%10.3f%10.3f%10.3f\n", xList.get(i), euilerYList.get(i), exactYList.get(i), diffList.get(i));
        }
    }

    public void calc() {
        double step = b - a;
        step /= (N - 1);
        xList.add(a);
        euilerYList.add(V + 2);

        for (int i = 1; i < N; i++) {
            xList.add(xList.get(i - 1) + step);
        }
        for (int i = 1; i < N; i++) {
            euilerYList.add(euilerYList.get(i - 1) + step * stepF(xList.get(i - 1), euilerYList.get(i - 1)));
        }
        for (int i = 0; i < N; i++) {
            double exactVal = origF(xList.get(i));
            exactYList.add(exactVal);
            diffList.add(Math.abs(exactVal - euilerYList.get(i)));
        }

        System.out.format("\tx\teuiler y\texact y\t\tdiff\n");
        for (int i = 0; i < N; i++) {
            System.out.format("%.3f%10.3f%10.3f%10.3f\n", xList.get(i), euilerYList.get(i), exactYList.get(i), diffList.get(i));
        }
    }


    public void pred_kor_calc() {
        double step = b - a;
        step /= (N - 1);
        xList.add(a);
        yList.add(V + 2);

        for (int i = 1; i < N; i++) {
            xList.add(xList.get(i - 1) + step);
        }

        for (int i = 1; i < xList.size(); i++) {
            double _tmpFx = stepF(xList.get(i - 1), yList.get(i - 1));
            double tmpFx = yList.get(i - 1) + step * stepF(xList.get(i - 1),yList.get(i - 1));
            double tmp = stepF(xList.get(i), tmpFx);
            double y = yList.get(i - 1) + step * (_tmpFx + tmp) / 2 ;
            yList.add(y);
        }

        for (int i = 0; i < N; i++) {
            double exactVal = origF(xList.get(i));
            exactYList.add(exactVal);
            diffList.add(Math.abs(exactVal - yList.get(i)));
        }

        System.out.format("\tx\tpred_kor y\texact y\t\tdiff\n");
        for (int i = 0; i < N; i++) {
            System.out.format("%.3f%10.3f%10.3f%10.3f\n", xList.get(i), yList.get(i), exactYList.get(i), diffList.get(i));
        }

    }
}

public class CauchyEuilerSolve {
    public static void main(String[] args) {
        EuilerSolve es = new EuilerSolve();
        es.calc();
        System.out.println("===========");
        EuilerSolve esImpr = new EuilerSolve();
        esImpr.calcImproved();
        EuilerSolve pred_kor = new EuilerSolve();
        pred_kor.pred_kor_calc();
    }
}